A317366 Expansion of e.g.f. exp(exp(x/(1 - x)) - 1)/(1 - x).

1, 2, 8, 47, 359, 3347, 36665, 460098, 6494444, 101708007, 1748263435, 32697711895, 660642793717, 14332871438810, 332186039584768, 8188070581358795, 213821204277955267, 5895325327054011087, 171095582314380667621, 5212792218964517899506, 166321395872186089502972, 5545223090189205308551443

Offset: 0

Author

Ilya Gutkovskiy, Jul 26 2018

Keywords

• nonn

Crossrefs

Cf. A000110, A002720, A084357, A101053.

Programs

Maple

a:= proc(n) option remember; add(binomial(n, k)^2
      *k!*combinat[bell](n-k), k=0..n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 26 2018

Mathematica

nmax = 21; CoefficientList[Series[Exp[Exp[x/(1 - x)] - 1]/(1 - x) , {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k]^2 k! BellB[n - k], {k, 0, n}], {n, 0, 21}]

Formula

a(n) = Sum_{k=0..n} binomial(n,k)^2*k!*Bell(n-k), where Bell() = A000110.