A355128 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (exp(x) - 1)).

1, 1, 4, 54, 1928, 167770, 34128972, 15867798142, 16621680303888, 38813463431274402, 200266228576991017940, 2265670919773168963168454, 55816752493202168837392763544, 2976116188645489878229876218205674, 341574630434025162744892242114482410332

Offset: 0

Author

Seiichi Manyama, Jun 20 2022

Keywords

• nonn

Crossrefs

Cf. A048801, A355100, A355131.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(j=0, i-1, 2^j*stirling(i-1, j, 2)*v[j+1])); v;

Formula

a(0) = 1; a(n) = n * Sum_{k=0..n-1} 2^k * Stirling2(n-1,k) * a(k).

a(n) = n * A355131(n-1) for n>0.