A381649 G.f. A(x) satisfies A(x) = 1 + x * A(x)^2 * A(x*A(x)^3)^3.

1, 1, 5, 44, 510, 7024, 109362, 1871530, 34590180, 682396379, 14251399805, 313170119013, 7207845252630, 173129413258492, 4327373963163746, 112289379643018983, 3018922654575996866, 83951253980821314446, 2411137697712963195801, 71427857356498491780290

Offset: 0

Author

Seiichi Manyama, Mar 03 2025

Keywords

• nonn

Crossrefs

Column k=1 of A381648.

Cf. A120973, A212029, A381601, A381615.

Cf. A087949, A381029.

Programs

PARI

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

Formula

See A381648.