A337467 Expansion of sqrt(2 / ( (1-2*x+49*x^2) * (1-7*x+sqrt(1-2*x+49*x^2)) )).

1, 3, -21, -139, 531, 6489, -9723, -292293, -135117, 12514313, 29905809, -501239553, -2310673379, 18245192679, 140574917259, -562805403867, -7557237645741, 11275709877369, 371974318253601, 201852054629631, -16932135947326551, -42530838930147813, 709138646702505999

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} (-3)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).

a(0) = 1, a(1) = 3 and n * (2*n+1) * (4*n-3) * a(n) = (4*n-1) * (4*n^2-2*n+1) * a(n-1) - 49 * (n-1) * (2*n-1) * (4*n+1) * a(n-2) for n > 1. - Seiichi Manyama, Aug 29 2020

Mathematica

a[n_] := Sum[(-3)^(n-k) * Binomial[2*k, k] * Binomial[2*n+1, 2*k], {k, 0, n}]; Array[a, 23, 0] (* Amiram Eldar, Apr 29 2021 *)

Prog

(PARI) N=40; x='x+O('x^N); Vec(sqrt(2/((1-2*x+49*x^2)*(1-7*x+sqrt(1-2*x+49*x^2)))))
(PARI) {a(n) = sum(k=0, n, (-3)^(n-k)*binomial(2*k, k)*binomial(2*n+1, 2*k))}

Crossrefs

Column k=3 of A337464.

Cf. A245927, A337422.

Sequence in context: A346935 A137969 A303349 * A318041 A054419 A228115

Adjacent sequences: A337464 A337465 A337466 * A337468 A337469 A337470

Keyword

sign

Author

Seiichi Manyama, Aug 28 2020

Status

approved