A385942 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^5) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 5, 508, 497861, 2554041696, 47918955042217, 2608995595530944320, 350836859825187730934697, 103472315352121087796983183360, 61101436986101317921145771113951181, 67212924933426575369862458525709786073344, 129898118403746997254471428114728554653243564525

Offset: 0

Author

Seiichi Manyama, Jul 13 2025

Keywords

• nonn

Crossrefs

Cf. A156326, A385939, A385940, A385941, A385943.

Cf. A385833.

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^5)*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..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).