A351428 Expansion of e.g.f. 1/exp(exp(exp(exp(exp(x)-1)-1)-1)-1).

1, -1, -3, -11, -41, -75, 1540, 37725, 657715, 10551750, 163089430, 2407275470, 31865298262, 290682880132, -2479867505029, -267542605513289, -11438897571729494, -404343336811199242, -13192591498632627584, -410340915410006575406, -12233989907129223814578

Offset: 0

Author

Seiichi Manyama, Feb 11 2022

Keywords

• sign

Crossrefs

Column k=5 of A351429.

Cf. A000587, A130410, A351427.

Cf. A000357, A351423.

Programs

Maple

g:= x-> exp(x)-1:
a:= n-> n! * coeff(series(1/((g@@5)(x)+1), x, n+1), x, n):
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 11 2022

Mathematica

T[n_, 0] := (-1)^n * n!; T[n_, k_] := T[n, k] = Sum[StirlingS2[n, j]*T[j, k - 1], {j, 0, n}]; a[n_] := T[n, 5]; Array[a, 20, 0] (* Amiram Eldar, Feb 11 2022 *)
With[{nn=20},CoefficientList[Series[1/Exp[Exp[Exp[Exp[Exp[x]-1]-1]-1]-1],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 09 2025 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/exp(exp(exp(exp(exp(x)-1)-1)-1)-1)))

PARI

T(n, k) = if(k==0, (-1)^n*n!, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
a(n) = T(n, 5);

Formula

a(n) = T(n,5), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = (-1)^n * n!.