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.

Showing 1-2 of 2 results.

A100521 Denominator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2.

Original entry on oeis.org

1, 4, 72, 1200, 19600, 635040, 25613280, 82450368, 9275666400, 595703908800, 2048086772160, 23459903026560, 413676290035008, 4419618483280000, 3221901874311120000, 361282596839420256000, 2630246784565779288000, 9628029406360113091200, 1310481780310126504080000
Offset: 0

Views

Author

N. J. A. Sloane, Nov 25 2004

Keywords

Examples

			1, 7/4, 137/72, 2341/1200, 38629/19600, 1257937/635040, 50881679/25613280, 164078209/82450368, 18480100619/9275666400, 1187779852639/595703908800, ... = A100520/A100521

Links

Crossrefs

Cf. A100520.

Programs

  • Magma
    [Denominator( (&+[(-1)^k/Binomial(2*n,k)^2: k in [0..2*n]]) ): n in [0..30]]; // G. C. Greubel, Jun 25 2022
  • Mathematica
    Table[Denominator[Sum[(-1)^k/Binomial[2*n,k]^2, {k,0,2*n}]], {n,0,30}] (* G. C. Greubel, Jun 25 2022 *)
  • PARI
    a(n) = denominator(sum(k=0, 2*n, (-1)^k/binomial(2*n, k)^2)); \\ Michel Marcus, Jun 25 2022
  • SageMath
    [denominator(sum((-1)^k/binomial(2*n,k)^2 for k in (0..2*n))) for n in (0..30)] # G. C. Greubel, Jun 25 2022

Formula

a(n) = denominator( Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2 ).

Extensions

Definition corrected by Alexander Adamchuk, May 11 2007

A122184 Numerator of Sum_{k=0..2n} (-1)^k/C(2n,k)^3.

Original entry on oeis.org

1, 15, 1705, 47789, 1369377, 213162301, 43005554527, 14505995375, 23869750002797, 2384790127843063, 624724994927411, 24386251366041479501, 2042595777439018142725, 11191251831905709132993
Offset: 0

Views

Author

Alexander Adamchuk, May 10 2007

Keywords

Comments

p^k divides a((p^k+1)/2) for prime p>2 and integer k>0.

Links

Crossrefs

Cf. A046825 = Numerator of Sum_{k=0..n} 1/C(n, k). Cf. A100516 = Numerator of Sum_{k=0..n} 1/C(n, k)^2. Cf. A100518 = Numerator of Sum_{k=0..n} 1/C(n, k)^3. Cf. A100520 = Numerator of Sum_{k=0..2n} (-1)^k/C(2n, k)^2.

Programs

  • Mathematica
    Table[ Numerator[ Sum[ (-1)^k / Binomial[2n,k]^3, {k,0,2n} ] ], {n,0,25} ]

Formula

a(n) = Numerator[ Sum[ (-1)^k / Binomial[2n,k]^3, {k,0,2n} ] ].
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.