cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A017808 Binomial coefficients C(92,n).

Original entry on oeis.org

1, 92, 4186, 125580, 2794155, 49177128, 713068356, 8760554088, 93080887185, 868754947060, 7210666060598, 53752237906276, 362827605867363, 2232785266876080, 12599288291657880, 65516299116620976, 315297189498738447, 1409563905994360116
Offset: 0

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Row 92 of A007318.

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A017809 Binomial coefficients C(93,n).

Original entry on oeis.org

1, 93, 4278, 129766, 2919735, 51971283, 762245484, 9473622444, 101841441273, 961835834245, 8079421007658, 60962903966874, 416579843773639, 2595612872743443, 14832073558533960, 78115587408278856, 380813488615359423, 1724861095493098563
Offset: 0

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Row 93 of A007318.

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A017810 Binomial coefficients C(94,n).

Original entry on oeis.org

1, 94, 4371, 134044, 3049501, 54891018, 814216767, 10235867928, 111315063717, 1063677275518, 9041256841903, 69042324974532, 477542747740513, 3012192716517082, 17427686431277403, 92947660966812816, 458929076023638279, 2105674584108457986
Offset: 0

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Row 94 of A007318.

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A017811 Binomial coefficients C(95,n).

Original entry on oeis.org

1, 95, 4465, 138415, 3183545, 57940519, 869107785, 11050084695, 121550931645, 1174992339235, 10104934117421, 78083581816435, 546585072715045, 3489735464257595, 20439879147794485, 110375347398090219, 551876736990451095
Offset: 0

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Row 95 of A007318.

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A017812 Binomial coefficients C(96,n).

Original entry on oeis.org

1, 96, 4560, 142880, 3321960, 61124064, 927048304, 11919192480, 132601016340, 1296543270880, 11279926456656, 88188515933856, 624668654531480, 4036320536972640, 23929614612052080, 130815226545884704, 662252084388541314, 3116480397122547360
Offset: 0

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Row 96 of A007318.

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A017813 Binomial coefficients C(97,n).

Original entry on oeis.org

1, 97, 4656, 147440, 3464840, 64446024, 988172368, 12846240784, 144520208820, 1429144287220, 12576469727536, 99468442390512, 712857170465336, 4660989191504120, 27965935149024720, 154744841157936784, 793067310934426018, 3778732481511088674
Offset: 0

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Row 97 of A007318.

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A017814 Binomial coefficients C(98,n).

Original entry on oeis.org

1, 98, 4753, 152096, 3612280, 67910864, 1052618392, 13834413152, 157366449604, 1573664496040, 14005614014756, 112044912118048, 812325612855848, 5373846361969456, 32626924340528840, 182710776306961504, 947812152092362802, 4571799792445514692
Offset: 0

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Row 98 of A007318.

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A017815 Binomial coefficients C(99,n).

Original entry on oeis.org

1, 99, 4851, 156849, 3764376, 71523144, 1120529256, 14887031544, 171200862756, 1731030945644, 15579278510796, 126050526132804, 924370524973896, 6186171974825304, 38000770702498296, 215337700647490344, 1130522928399324306, 5519611944537877494
Offset: 0

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Row 99 of A007318.

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A017766 Binomial coefficients C(50,n).

Original entry on oeis.org

1, 50, 1225, 19600, 230300, 2118760, 15890700, 99884400, 536878650, 2505433700, 10272278170, 37353738800, 121399651100, 354860518600, 937845656300, 2250829575120, 4923689695575, 9847379391150, 18053528883775, 30405943383200, 47129212243960
Offset: 0

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Row 50 of A007318.

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Formula

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^50.
E.g.f.: 1F1(-50; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017769 Binomial coefficients C(53,n).

Original entry on oeis.org

1, 53, 1378, 23426, 292825, 2869685, 22957480, 154143080, 886322710, 4431613550, 19499099620, 76223753060, 266783135710, 841392966470, 2403979904200, 6250347750920, 14844575908435, 32308782859535, 64617565719070, 119032357903550, 202355008436035
Offset: 0

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Row 53 of A007318.

Crossrefs

Programs

  • Magma
    [Binomial(53,n): n in [0..53]]; // G. C. Greubel, Nov 13 2018
  • Maple
    seq(binomial(53,n), n=0..53); # Nathaniel Johnston, Jun 24 2011
  • Mathematica
    With[{k = 53}, Array[Binomial[k, #] &, k + 1, 0]] (* Michael De Vlieger, Jul 06 2018 *)
    With[{nmax = 53}, CoefficientList[Series[Hypergeometric1F1[-53, 1, -x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 13 2018 *)
  • PARI
    vector(53, n, n--; binomial(53,n)) \\ G. C. Greubel, Nov 13 2018
    
  • Sage
    [binomial(53, n) for n in range(54)] # Zerinvary Lajos, May 23 2009
    

Formula

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^53.
E.g.f.: 1F1(-53; 1; -x), where 1F1 is the confluent hypergeometric function. (End)
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