A360085 a(n) = Sum_{k=0..n} (-1)^k * binomial(4*k,n-k) * Catalan(k).

1, -1, -2, 5, 6, -37, 12, 236, -454, -1038, 5258, -688, -41780, 79528, 212032, -1067717, 99414, 9232114, -17976592, -49506598, 255604634, -28864080, -2294742268, 4618754686, 12550067560, -67132100862, 10660021188, 612813797856, -1280237246540, -3357371054108

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Formula

G.f. A(x) satisfies A(x) = 1/(1 + x * (1+x)^4 * A(x)).

G.f.: 2 / (1 + sqrt( 1 + 4*x*(1+x)^4 )).

Prog

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

Crossrefs

Cf. A360084, A360086.

Cf. A000108.

Sequence in context: A365085 A164805 A275285 * A152918 A276845 A365503

Adjacent sequences: A360082 A360083 A360084 * A360086 A360087 A360088

Keyword

sign

Author

Seiichi Manyama, Jan 25 2023

Status

approved