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%I #12 Oct 31 2024 13:12:38
%S 1,2,10,66,560,5770,69852,970886,15228880,266006610,5119447700,
%T 107617719022,2453167135608,60268223308826,1587381621990556,
%U 44619277892537910,1333135910963656352,42189279001183102882,1409741875877923927332,49597905017847180008126
%N Expansion of e.g.f. 1/(1 - x * exp(x))^2.
%F a(n) = n! * Sum_{k=0..n} (k+1) * k^(n-k)/(n-k)!.
%F a(n) ~ n! * n/((1 + LambertW(1))^2 * LambertW(1)^n). - _Vaclav Kotesovec_, Oct 31 2024
%o (PARI) a(n) = n!*sum(k=0, n, (k+1)*k^(n-k)/(n-k)!);
%Y Cf. A006153, A377530.
%Y Cf. A377503, A377527.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Oct 30 2024