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%I #12 May 21 2022 08:41:08
%S 1,0,4,6,56,250,1812,12614,101040,864882,7988780,78726142,823897032,
%T 9111774698,106068603396,1295153135670,16538681229152,220281968528098,
%U 3053087839536732,43941561067048430,655501502129291640,10118103843683127642
%N Expansion of e.g.f. exp( 2 * x * (exp(x) - 1) ).
%F a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * Stirling2(n-k,k)/(n-k)!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x*(exp(x)-1))))
%o (PARI) a(n) = n!*sum(k=0, n\2, 2^k*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A052506, A351734.
%Y Cf. A053489, A351736.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 20 2022
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