A376810 Expansion of 1/sqrt(1 - 4*x/(1 - x^2)^2).

1, 2, 6, 24, 94, 378, 1544, 6380, 26598, 111658, 471358, 1998924, 8509368, 36341278, 155634228, 668116136, 2874157222, 12387209982, 53475080494, 231189987224, 1000834283190, 4337864724462, 18821884379924, 81748960355484, 355383570351664, 1546239230878154

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k-1,k) * binomial(2*n-4*k,n-2*k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^2)^2))
(PARI) a(n) = sum(k=0, n\2, binomial(2*n-3*k-1, k)*binomial(2*n-4*k, n-2*k));

Crossrefs

Cf. A110170, A376811.

Cf. A349713.

Sequence in context: A375276 A374598 A361752 * A115220 A293185 A292984

Adjacent sequences: A376807 A376808 A376809 * A376811 A376812 A376813

Keyword

nonn

Author

Seiichi Manyama, Oct 04 2024

Status

approved