A360086 a(n) = Sum_{k=0..n} (-1)^k * binomial(5*k,n-k) * Catalan(k).

1, -1, -3, 5, 19, -52, -114, 570, 470, -6026, 2156, 59311, -93869, -519805, 1668241, 3635670, -23289426, -11134840, 280455900, -238282316, -2944763030, 6683843250, 25804836482, -113673966635, -155130413515, 1570407337023, -253144380823, -18639853806224

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f. A(x) satisfies A(x) = 1/(1 + x * (1+x)^5 * A(x)).

G.f.: 2 / (1 + sqrt( 1 + 4*x*(1+x)^5 )).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(5*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)^5)))

Crossrefs

Cf. A360084, A360085.

Cf. A000108.

Sequence in context: A209778 A148546 A148547 * A127998 A174132 A106918

Adjacent sequences: A360083 A360084 A360085 * A360087 A360088 A360089

Keyword

sign

Author

Seiichi Manyama, Jan 25 2023

Status

approved