A354729 E.g.f. A(x) satisfies A(x) = 1 + x * A(log(1+x)).

1, 1, 2, 3, -4, -30, 234, 679, -35848, 305208, 6762360, -290545486, 2866197828, 186075548048, -10575881477630, 151622861284395, 14937532353298992, -1269964031741331704, 32904195657758601624, 2814524425307181390432, -395787864674458924551840

Offset: 0

Author

Seiichi Manyama, Jun 04 2022

Keywords

• sign

Crossrefs

Cf. A048801, A354728, A354730.

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, stirling(i-1, j, 1)*v[j+1])); v;

Formula

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

a(n) = n * A354728(n-1) for n>0.