%I #11 Jun 26 2022 08:58:01

%S 1,4,18,90,494,2946,18926,130066,950654,7353794,59954638,513333618,

%T 4601380766,43062556322,419742815726,4252083713874,44680229906622,

%U 486145710591874,5468499473222670,63503107472489266,760281866742088670,9373065303624742498,118858898763010225198

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

%H Vaclav Kotesovec, <a href="/A355247/b355247.txt">Table of n, a(n) for n = 0..550</a>

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

%F a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k+1) * Bell(n-k+1). - _Ilya Gutkovskiy_, Jun 26 2022

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

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

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jun 25 2022