A100520 Numerator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2.

1, 7, 137, 2341, 38629, 1257937, 50881679, 164078209, 18480100619, 1187779852639, 4086043585673, 46823724627623, 825926870076593, 8826243587390221, 6435629123661395137, 721766119107018403553, 5255377541226932317019, 19239461977895120106181, 2618947765106118753941303

Offset

0,2

Links

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

Formula

a(n) = numerator( 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[Numerator[Sum[(-1)^k/Binomial[2*n, k]^2, {k, 0, 2*n}]], {n, 0, 30}] (* G. C. Greubel, Jun 24 2022 *)

Prog

(Magma) [Numerator( (&+[(-1)^k/Binomial(2*n, k)^2: k in [0..2*n]]) ): n in [0..30]]; // G. C. Greubel, Jun 24 2022
(SageMath) [numerator(sum((-1)^k/binomial(2*n, k)^2 for k in (0..2*n))) for n in (0..30)] # G. C. Greubel, Jun 24 2022
(PARI) a(n) = numerator(sum(k=0, 2*n, (-1)^k/binomial(2*n, k)^2)); \\ Michel Marcus, Jun 25 2022

Crossrefs

Cf. A100516, A100521.

Sequence in context: A220380 A051504 A058881 * A221342 A221298 A009701

Adjacent sequences: A100517 A100518 A100519 * A100521 A100522 A100523

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 25 2004

Extensions

Definition corrected by Alexander Adamchuk, May 11 2007

Status

approved