A366589 G.f. A(x) satisfies A(x) = 1 + x^4*(1+x)*A(x)^2.

1, 0, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 5, 15, 15, 5, 14, 56, 84, 56, 56, 210, 420, 420, 342, 834, 1980, 2640, 2409, 3795, 9141, 15015, 16445, 20449, 43043, 80509, 104962, 123838, 215072, 419848, 630838, 780572, 1164228, 2190552, 3629704, 4884100, 6760390, 11715210

Offset

0,9

Links

Table of n, a(n) for n=0..47.

Formula

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

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

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(2*k, k)/(k+1));

Crossrefs

Cf. A115178, A366588.

Cf. A366554.

Sequence in context: A258711 A127278 A356165 * A335764 A202069 A364529

Adjacent sequences: A366586 A366587 A366588 * A366590 A366591 A366592

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2023

Status

approved