A386508 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^5 * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 3, 295, 287917, 1475577461, 27675935977381, 1506650312499716245, 202590228421127415254121, 59748112811137686928254493705, 35281260624146463343889980853779081, 38809774783723742261321649306513968984201, 75004702183951627532765950774478944180316824189

Offset: 0

Author

Seiichi Manyama, Jul 24 2025

Keywords

• nonn

Crossrefs

Cf. A143925, A386505, A386506, A386507, A386509.

Cf. A385942, A386446.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*j^5*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).