A381595 G.f. A(x) satisfies A(x) = 1/(1 - x * A(x) * A(x*A(x)))^3.

1, 3, 24, 280, 4044, 67365, 1246534, 25051422, 538836147, 12279937669, 294374405652, 7382843258466, 192917842671564, 5235276617405133, 147163222059602313, 4275948043251399950, 128196303568520249238, 3959890522003241945409, 125863828745364900374059

Offset: 0

Author

Seiichi Manyama, Mar 01 2025

Keywords

• nonn

Crossrefs

Column k=3 of A381594.

Cf. A088714, A381593.

Cf. A145160, A381574, A381601.

Programs

PARI

a(n, k=3) = 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 A381594.

G.f.: B(x)^3, where B(x) is the g.f. of A381601.