A337465 a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).

1, 5, -6, -139, 1654, -5853, -196860, 6258751, -112580442, 985287863, 26443436876, -1897380617625, 72596047613116, -2086036395460171, 39493340495025864, 304974352009838745, -85532651616832374010, 6040114369000387188975, -321378391411642082323524, 14224299551865677212271567

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Mathematica

a[n_] := Sum[If[n == n - k == 0, 1, (-n)^(n-k)] * Binomial[2*k, k] * Binomial[2*n+1, 2*k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Apr 29 2021 *)

Prog

(PARI) {a(n) = sum(k=0, n, (-n)^(n-k)*binomial(2*k, k)*binomial(2*n+1, 2*k))}

Crossrefs

Main diagonal of A337464.

Cf. A337387, A337420.

Sequence in context: A078984 A266718 A041257 * A041411 A103089 A041601

Adjacent sequences: A337462 A337463 A337464 * A337466 A337467 A337468

Keyword

sign

Author

Seiichi Manyama, Aug 28 2020

Status

approved