A351427 Expansion of e.g.f. 1/exp(exp(exp(exp(x)-1)-1)-1).

1, -1, -2, -4, -2, 76, 953, 9103, 77054, 550457, 2123247, -32551171, -1197444063, -26019611323, -478608682879, -7915791047153, -115777452314939, -1320533985179144, -3550854626237496, 455708391448493954, 21276221692251262984, 703173682906460544467

Offset: 0

Author

Seiichi Manyama, Feb 11 2022

Keywords

• sign

Crossrefs

Column k=4 of A351429.

Cf. A000587, A130410, A351428.

Cf. A000307, A351422.

Programs

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, 4]; Array[a, 22, 0] (* Amiram Eldar, Feb 11 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/exp(exp(exp(exp(x)-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, 4);

Formula

a(n) = T(n,4), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = (-1)^n * n!.