A386450 G.f. A(x) satisfies A(x) = 1/(1 - x - x^5*A''''(x)).

1, 1, 1, 1, 1, 25, 3049, 1103713, 929323297, 1563120681841, 4730002253928145, 23848669801185169825, 188929157434986723256801, 2244856224793842495701519113, 38526222340982767558002054899641, 925631015719595748793089592291450945, 30325523298479173582153602405524578371265

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386448, A386449, A386451.

Cf. A385764.

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, sum(k=1, 4, stirling(4, k, 1)*j^k)*v[j+1]*v[i-j])); v;

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).