A358031 Expansion of e.g.f. (1 - log(1-x))/(1 + log(1-x) * (1 - log(1-x))).

1, 2, 8, 52, 450, 4878, 63474, 963744, 16724016, 326497632, 7082393136, 168995017200, 4399028766192, 124051494462816, 3767315220903072, 122581568808533760, 4254486275273419008, 156890997080103149568, 6125936704495619486976, 252480641031903073955328

Offset: 0

Author

Seiichi Manyama, Oct 25 2022

Keywords

• nonn

Crossrefs

Cf. A354013, A354018.

Cf. A000557, A358032.

Programs

Maple

f:= proc(n) local k; add(k!*combinat:-fibonacci(k+2)*abs(Stirling1(n,k)),k=0..n) end proc:
map(f, [$0..30]); # Robert Israel, Oct 25 2022

Mathematica

With[{nn=20},CoefficientList[Series[(1-Log[1-x])/(1+Log[1-x](1-Log[1-x])),{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Jan 25 2024 *)

PARI

my(N=20, 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)*abs(stirling(n, k, 1)));

Formula

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

a(n) = A354013(n) + A354018(n).