A385941 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^4) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 5, 268, 88997, 114813696, 431933720137, 3924557764490560, 75445736579647162857, 2782590090487142758353280, 182621397948270167786531824781, 20092371907364577184989521575079424, 3530551258386563793887714321816262653965, 951815440668013126114976449397609983348430848

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A156326, A385939, A385940, A385942, A385943.

Cf. A385832.

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)*(1+j^4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( x*A(x) + x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ).