A358032 Expansion of e.g.f. (1 + log(1+x))/(1 - log(1+x) * (1 + log(1+x))).

1, 2, 4, 16, 66, 438, 2694, 25296, 204576, 2509728, 24912816, 381010320, 4440815472, 82150191264, 1089159690912, 23879423005440, 351430312958208, 9005004020293632, 144184020764472576, 4277182103330660352, 73227226213747521792, 2499666592623881921280

Offset: 0

Author

Seiichi Manyama, Oct 25 2022

Keywords

• nonn

Crossrefs

Cf. A005444, A005445.

Cf. A000557, A358031.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace((1+log(1+x))/(1-log(1+x)*(1+log(1+x)))))

PARI

a(n) = sum(k=0, n, k!*fibonacci(k+2)*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} k! * Fibonacci(k+2) * Stirling1(n,k).

a(n) = A005444(n) + A005445(n).