A355120 E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2 * log(1+x)).

1, 1, 3, 26, 654, 45084, 7934924, 3381663872, 3365978050576, 7632454575648720, 38732162420625498608, 434139952882119137261024, 10640704036253473615712677216, 565765176687479152385624223741568, 64834956096893473256448986077914291328

Offset: 0

Author

Seiichi Manyama, Jun 20 2022

Keywords

• nonn

Crossrefs

Cf. A354728, A355084, A355096, A355133.

Programs

PARI

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

Formula

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

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