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%I #18 Aug 09 2022 00:15:49
%S 1,0,1,8,93,1354,23900,496244,11855700,320428318,9667220397,
%T 322072882348,11744421711587,465270864839688,19899234175413257,
%U 913836170567749048,44849438199960187278,2342666125012348876152
%N Number of labeled digraphs with n arcs and with no vertex of indegree 0.
%F a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*A122418(k).
%F G.f.: Sum_{n>=0} ((1+x)^(n-1) - 1)^n.
%F a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491726382774188556341627278..., r = 0.8737024332396683304965683047207192982139922672025395099... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0, and c = 0.08904589343883135100956914504938... . - _Vaclav Kotesovec_, May 07 2014
%p A122418 := proc(n) option remember ; add( combinat[stirling2](n,k)*(k-1)^n*k!,k=0..n) ; end: A122419 := proc(n) option remember ; add( combinat[stirling1](n,k)*A122418(k),k=0..n)/n! ; end: for n from 0 to 30 do printf("%d, ",A122419(n)) ; od ; # _R. J. Mathar_, May 18 2007
%t nmax=20; CoefficientList[Series[Sum[((1+x)^(n-1)-1)^n, {n, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 06 2014 *)
%Y Cf. A122420, A122400.
%K easy,nonn
%O 0,4
%A _Vladeta Jovovic_, Sep 03 2006
%E More terms from _R. J. Mathar_, May 18 2007
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