帕斯卡三角形與11的幂

帕斯卡三角形

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

1 10 45 120 210 252 210 120 45 10 1

1 11 55 165 330 462 462 330 165 55 11 1

1 12 66 220 495 792 924 792 495 220 66 12 1

1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1

1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1

1 15 105 455 1365 3003 5005 6435 6435 5005 3003 1365 455 105 15 1

1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1

1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1

1 18 153 816 3060 8568 18564 31824 43758 48620 43758 31824 18564 8568 3060 816 153 18 1

1 19 171 969 3876 11628 27132 50388 75582 92378 92378 75582 50388 27132 11628 3876 969 171 19 1

1 20 190 1140 4845 15504 38760 77520 125970 167960 184756 167960 125970 77250 38760 15504 4845 1140 190 20 1

1 21 210 1330 5985 20349 54264 116280 203490 293930 352716 352716 293930 203490 116280 54264 20349 5985 1330 210 21 1

1 22 231 1540 7315 26334 74613 170544 319770 497420 646646 705432 646646 497420 319770 170544 74613 26334 7315 1540 231 22 1

1 23 253 1771 8855 33649 100947 245157 490314 817190 1144066 1352078 1352078 1144066 817190 490314 245157 100947 33649 8855 1771 253 23 1

1 24 276 2024 10626 42504 134596 346104 735471 1307504 1961256 2496144 2704156 2496144 1961256 1307504 735471 346104 134596 42504 10626 2024 276 24 1

1 25 300 2300 12650 53130 177100 480700 1081575 2042975 3268760 4457400 5200300 5200300 4457400 3268760 2042975 1081575 480700 177100 53130 12650 2300 300 25 1

1 26 325 2600 14950 65780 230230 657800 1562275 3124550 5311735 7726160 9657700 10400600 9657700 7726160 5311735 3124550 1562275 657800 230230 65780 14950 2600 325 26 1

1 27 351 2925 17550 80730 296010 888030 2220075 4686825 8436285 13037895 17383860 20058300 20058300 17383860 13037895 8436285 4686825 2220075 888030 296010 80730 17550 2925 351 27 1

1 28 378 3276 20475 98280 376740 1184040 3108105 6906900 13123110 21474180 30421755 37442160 40116600 37442160 30421755 21474180 13123110 6906900 3108105 1184040 376740 98280 20475 3276 378 28 1

1 29 406 3654 23751 118755 475020 1560780 4292145 10015005 20030010 34597290 51895935 67863915 77558760 77558760 67863915 51895935 34597290 20030010 10015005 4292145 1560780 475020 118755 23751 3654 406 29 1

1 30 435 4060 27405 142506 593775 2035800 5852925 14307150 30045015 54627300 86493225 119759850 145422675 155117520 145422675 119759850 86493225 54627300 30045015 14307150 5852925 2035800 593775 142506 27405 4060 435 30 1

1 31 465 4495 31465 169911 736281 2629575 7888725 20160075 44352165 84672315 141120525 206253075 265182525 300540195 300540195 265182525 206253075 141120525 84672315 44352165 20160075 7888725 2629575 736281 169911 31465 4495 465 31 1

1 32 496 4960 35960 201376 906192 3365856 10518300 28048800 64512240 129024480 225792840 347373600 471435600 565722720 601080390 565722720 471435600 347373600 225792840 129024480 64512240 28048800 10518300 3365856 906192 201376 35960 4960 496 32 1

1 33 528 5456 40920 237336 1107568 4272048 13884156 38567100 92561040 193536720 354817320 573166440 818809200 1037158320 1166803110 1166803110 1037158320 818809200 573166440 354817320 193536720 92561040 38567100 13884156 4272048 1107568 237336 40920 5456 528 33 1

11的冪

11⁰ = 1

11¹ = 11

11² = 121

11³ = 1331

11⁴ = 14641

11⁵ = 161051

11⁶ = 1771561

11⁷ = 19487171

11⁸ = 214358881

11⁹ = 2357947691

11¹⁰ = 25937424601

11¹¹ = 285311670611

11¹² = 3138428376721

11¹³ = 34522712143931

11¹⁴ = 379749833583241

11¹⁵ = 4177248169415651

11¹⁶ = 45949729863572161

11¹⁷ = 505447028499293771

11¹⁸ = 5559917313492231481

11¹⁹ = 61159090448414546291

11²⁰ = 672749994932560009201

11²¹ = 7400249944258160101211

11²² = 81402749386839761113321

11²³ = 895430243255237372246531

11²⁴ = 9849732675807611094711841

11²⁵ = 108347059433883722041830251

11²⁶ = 1191817653772720942460132761

11²⁷ = 13109994191499930367061460371

11²⁸ = 144209936106499234037676064081

11²⁹ = 1586309297171491574414436704891

11³⁰ = 17449402268886407318558803753801

11³¹ = 191943424957750480504146841291811

11³² = 2111377674535255285545615254209921

11³³ = 23225154419887808141001767796309131

11³⁴ = 255476698618765889551019445759400441

11³⁵ = 2810243684806424785061213903353404851

11³⁶ = 30912680532870672635673352936887453361

101的冪

101⁰ = 1

101¹ = 101

101² = 10201

101³ = 1030301

101⁴ = 104060401

101⁵ = 10510100501

101⁶ = 1061520150601

101⁷ = 107213535210701

101⁸ = 10828567056280801

101⁹ = 1093685272684360901

101¹⁰ = 110462212541120451001

101¹¹ = 11156683466653165551101

101¹² = 1126825030131969720661201

101¹³ = 113809328043328941786781301

101¹⁴ = 11494742132376223120464911401

101¹⁵ = 1160968955369998535166956051501

101¹⁶ = 117257864492369852051862561201601

101¹⁷ = 11843044313729355057238118681361701

101¹⁸ = 1196147475686664860781049986817531801

101¹⁹ = 120810895044353150938886048668570711901

101²⁰ = 12201900399479668244827490915525641902001

101²¹ = 1232391940347446492727576582468089832102101

101²² = 124471585975092095765485234829277073042312201

101²³ = 12571630183484301672314008717756984377273532301

1001的冪

1001⁰ = 1

1001¹ = 1001

1001² = 1002001

1001³ = 1003003001

1001⁴ = 1004006004001

1001⁵ = 1005010010005001

1001⁶ = 1006015020015006001

1001⁷ = 1007021035035021007001

1001⁸ = 1008028056070056028008001

1001⁹ = 1009036084126126084036009001

1001¹⁰ = 1010045120210252210120045010001

1001¹¹ = 1011055165330462462330165055011001

1001¹² = 1012066220495792924792495220066012001

1001¹³ = 1013078286716288717717287715286078013001

1001¹⁴ = 1014091365003005006434005003001364091014001

1001¹⁵ = 1015105456368008011441440008004365455105015001

1001¹⁶ = 1016120561824376019452881448012369820560120016001

1001¹⁷ = 1017136682386200395472334329460382190380680136017001

1001¹⁸ = 1018153819068586595867806663789842572571060816153018001

1001¹⁹ = 1019171972887655182463674470453632415143631876969171019001

10001的冪

10001⁰ = 1

10001¹ = 10001

10001² = 100020001

10001³ = 1000300030001

10001⁴ = 10004000600040001

10001⁵ = 100050010001000050001

10001⁶ = 1000600150020001500060001

10001⁷ = 10007002100350035002100070001

10001⁸ = 100080028005600700056002800080001

10001⁹ = 1000900360084012601260084003600090001

10001¹⁰ = 10010004501200210025202100120004500100001

10001¹¹ = 100110055016503300462046203300165005500110001

10001¹² = 1001200660220049507920924079204950220006600120001

10001¹³ = 10013007802860715128717161716128707150286007800130001

10001¹⁴ = 100140091036410012002300334323003200210010364009100140001

10001¹⁵ = 1001501050455136530035005643564355005300313650455010500150001

10001¹⁶ = 10016012005601820436880091441287114408008436818200560012000160001

10001¹⁷ = 100170136068023806189237794504312431194492376618823800680013600170001

10001¹⁸ = 1001801530816306085698567182837628624376118258564856830600816015300180001

10001¹⁹ = 10019017109693877163071370395559123872385558703907133162838760969017100190001