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

Author

N. J. A. Sloane, Nov 25 2004

Keywords

• nonn
• frac

Examples

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

Links

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

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