A381615 G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^3)^3).

1, 1, 4, 31, 320, 3969, 56080, 876204, 14860614, 270231265, 5223002719, 106613106181, 2287120272173, 51367948203527, 1204141944566399, 29385603693050274, 744943334951904519, 19580887642660810193, 532781828387893449124, 14984377196395037979472

Offset: 0

Author

Seiichi Manyama, Mar 01 2025

Keywords

• nonn

Crossrefs

Cf. A088714, A381029.

Cf. A120973, A212029, A381601.

Cf. A381574.

Programs

PARI

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

Formula

Let a(n,k) = [x^n] A(x)^k.

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