A386445 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} k^4 * a(k) * a(n-1-k).

1, 1, 2, 35, 2904, 749262, 469791130, 609789812623, 1465325443822620, 6004904311876287022, 39410188505158004325524, 394180711528456847821432318, 5771988198703021102520933624372, 119699491661363792184803354859998664, 3418976586120192927373434641290957978490

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386443, A386444, A386446, A386447.

Cf. A385832.

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

Formula

G.f. A(x) satisfies A(x) = 1/( 1 - x - x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ).