A355126 E.g.f. A(x) satisfies: A(x) = 1 + x * A(-2 * log(1-x)).

1, 1, 4, 54, 1936, 168780, 34360128, 15979581632, 16740281020160, 39091514910283872, 201702609432140369280, 2281926772696486970224192, 56217269029941735581289119232, 2997472083791372184890466743907712, 344025706673467887482938899075885442048

Offset: 0

Author

Seiichi Manyama, Jun 20 2022

Keywords

• nonn

Crossrefs

Cf. A354730, A355106, A355134.

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*abs(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 * A355134(n-1) for n>0.