A364723 G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^4).

1, 1, 2, 8, 38, 196, 1073, 6120, 35968, 216304, 1324676, 8232981, 51796538, 329229344, 2111031444, 13638557196, 88695018723, 580153216512, 3814285704000, 25192499164320, 167075960048996, 1112162062296061, 7428213584196010, 49766086788057256

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

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

Crossrefs

Cf. A000108, A106228, A300048, A364734.

Cf. A364739.

Sequence in context: A291088 A047098 A271934 * A372107 A266797 A369208

Adjacent sequences: A364720 A364721 A364722 * A364724 A364725 A364726

Keyword

nonn

Author

Seiichi Manyama, Aug 05 2023

Status

approved