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

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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..675

Formula

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

Example

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

Mathematica

Table[Denominator[Sum[(-1)^k/Binomial[2*n, k]^2, {k, 0, 2*n}]], {n, 0, 30}] (* G. C. Greubel, Jun 25 2022 *)

Prog

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

Crossrefs

Cf. A100520.

Sequence in context: A165212 A263219 A358295 * A111868 A060645 A363987

Adjacent sequences: A100518 A100519 A100520 * A100522 A100523 A100524

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 25 2004

Extensions

Definition corrected by Alexander Adamchuk, May 11 2007

Status

approved