A355124 E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * log(1+x)).

1, 1, 4, 42, 1168, 84180, 15107328, 6495857312, 6492989426432, 14753072834027424, 74941835564789489280, 840421638561217307501632, 20603672787268830442103493120, 1095629510349075557617215030858112, 125563465926494619940863277689861766144

Offset: 0

Author

Seiichi Manyama, Jun 20 2022

Keywords

• nonn

Crossrefs

Cf. A354729, A355104, A355133.

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, 1)*v[j+1])); v;

Formula

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

a(n) = n * A355133(n-1) for n>0.