A365186 G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^2).

1, 1, 6, 47, 428, 4241, 44407, 483358, 5414618, 62014112, 722870120, 8547768832, 102284029963, 1236274747490, 15070955944288, 185089043535730, 2287843817573898, 28440852786725695, 355345599519983962, 4459821165693379625, 56200963128262312342

Offset: 0

Author

Seiichi Manyama, Aug 25 2023

Keywords

• nonn

Crossrefs

Cf. A002295, A365184, A365185, A365187, A365188, A365189.

Cf. A365192.

Programs

PARI

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

Formula

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