A366176 G.f. A(x) satisfies A(x) = 1 + x*A(x)^3/(1 - x)^2.

1, 1, 5, 27, 161, 1030, 6921, 48190, 344669, 2517303, 18695908, 140771477, 1072130229, 8244820518, 63931532190, 499308229278, 3924204043333, 31012883225891, 246304580923299, 1964794017165157, 15735626383151876, 126476316316459089, 1019883740031357941

Offset: 0

Author

Seiichi Manyama, Oct 03 2023

Keywords

• nonn

Crossrefs

Partial sums give A199475.

Cf. A001764, A213282, A307678.

Programs

PARI

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

Formula

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