A355097 E.g.f. A(x) satisfies A(x) = 1 + 3 * log(1+x) * A(log(1+x)).

1, 3, 15, 87, 414, -333, -36207, -125415, 9692208, 65346480, -6686193834, -28979410023, 9399236141664, -74034590428035, -21601690453093869, 753341807730002715, 64208547156310265880, -6137571162315494165580, -131200755856066508312736

Offset: 0

Author

Seiichi Manyama, Jun 19 2022

Keywords

• sign

Crossrefs

Cf. A354728, A355096.

Cf. A355105.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*sum(j=1, i, j*stirling(i, j, 1)*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + 3*x*A(x).

a(0) = 1; a(n) = 3 * Sum_{k=1..n} k * Stirling1(n,k) * a(k-1).