A365756 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^3*A(x)^4).

1, 1, 1, 1, 2, 7, 22, 58, 142, 363, 1014, 2966, 8645, 24824, 71189, 206742, 609159, 1809493, 5388804, 16073002, 48092377, 144532884, 436168716, 1320372837, 4006489208, 12183544414, 37132838866, 113426618425, 347191793705, 1064688271730, 3270387354434

Offset: 0

Author

Seiichi Manyama, Sep 18 2023

Keywords

• nonn

Crossrefs

Cf. A023432, A212383, A365243, A365757.

Cf. A063019.

Programs

PARI

a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(n+k+1, n-3*k)/(n+k+1));

Formula

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