A363008 Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(x) - 1) - 1) - 1)).

1, 1, 6, 52, 594, 8444, 143783, 2854261, 64735570, 1651560175, 46814933977, 1459689346911, 49650414218071, 1829560770160335, 72603137881845927, 3086932915850946633, 139999909097319319787, 6746170002325663539844, 344199636595620793896784

Offset: 0

Author

Seiichi Manyama, May 12 2023

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..383

Crossrefs

Row p=4 of A153278 (for n>=1).

Column k=4 of A363007.

Cf. A351427.

Programs

Maple

b:= proc(n, m, t) option remember; `if`(n=0, `if`(t=1, m!,
      b(m, 0, t-1)), m*b(n-1, m, t)+b(n-1, m+1, t))
    end:
a:= n-> b(n, 0, 4):
seq(a(n), n=0..20);  # Alois P. Heinz, May 12 2023

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(exp(x)-1)-1)-1))))

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) = n!.