A385831 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^3) * a(k) * a(n-1-k).

1, 1, 3, 32, 961, 64467, 8255248, 1808137854, 625644428013, 322212826476551, 235861774406899499, 236570361788785389414, 315585587694401993913716, 546279374467805677562555764, 1201815582876341559500261276952, 3301389061225358326490572037897646

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A088716, A385830, A385832, A385833, A385834.

Cf. A385763.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j^3)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) - x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ).