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A317366
Expansion of e.g.f. exp(exp(x/(1 - x)) - 1)/(1 - x).
1
1, 2, 8, 47, 359, 3347, 36665, 460098, 6494444, 101708007, 1748263435, 32697711895, 660642793717, 14332871438810, 332186039584768, 8188070581358795, 213821204277955267, 5895325327054011087, 171095582314380667621, 5212792218964517899506, 166321395872186089502972, 5545223090189205308551443
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} binomial(n,k)^2*k!*Bell(n-k), where Bell() = A000110.
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 26 2018
STATUS
approved