A366677 G.f. satisfies A(x) = 1 + x^4 + x*A(x)^4.

1, 1, 4, 22, 141, 973, 7112, 54040, 422552, 3377770, 27478568, 226753828, 1893462584, 15969598554, 135842638632, 1164075017512, 10039732285528, 87081507756245, 759128176746864, 6647475055207618, 58445784269830824, 515745587816906733

Offset: 0

Author

Seiichi Manyama, Oct 16 2023

Keywords

• nonn

Crossrefs

Cf. A176697, A366676.

Cf. A366267, A366558.

Programs

PARI

a(n) = sum(k=0, n\4, binomial(3*(n-4*k)+1, k)*binomial(4*(n-4*k), n-4*k)/(3*(n-4*k)+1));

Formula

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