A355096 E.g.f. A(x) satisfies A(x) = 1 + 2 * log(1+x) * A(log(1+x)).

1, 2, 6, 16, -12, -492, 628, 63488, -408112, -20183928, 444216616, 9449212584, -679737200176, 2572902869080, 1276955484043864, -53294396490490656, -1891642613896659904, 314259171327032640928, -8590801196259162852288, -1381246455381881103425424

Offset: 0

Author

Seiichi Manyama, Jun 19 2022

Keywords

• sign

Crossrefs

Cf. A354728, A355097.

Cf. A355104.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, j*stirling(i, j, 1)*v[j])); v;

Formula

E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + 2*x*A(x).

a(0) = 1; a(n) = 2 * Sum_{k=1..n} k * Stirling1(n,k) * a(k-1).