A355247 - OEIS

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A355247

Expansion of e.g.f. exp(2*(exp(x) - 1 + x)).

1, 4, 18, 90, 494, 2946, 18926, 130066, 950654, 7353794, 59954638, 513333618, 4601380766, 43062556322, 419742815726, 4252083713874, 44680229906622, 486145710591874, 5468499473222670, 63503107472489266, 760281866742088670, 9373065303624742498, 118858898763010225198

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..550

FORMULA

a(n) ~ n^(n+2) * exp(n/LambertW(n/2) - n - 2) / (4 * sqrt(1 + LambertW(n/2)) * LambertW(n/2)^(n+2)).

a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k+1) * Bell(n-k+1). - Ilya Gutkovskiy, Jun 26 2022

MATHEMATICA

nmax = 25; CoefficientList[Series[Exp[2*Exp[x]-2+2*x], {x, 0, nmax}], x] * Range[0, nmax]!

CROSSREFS

Cf. A000110, A001861, A035009, A194689, A217924, A293024, A339014.