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%I #16 Jan 28 2024 20:34:53
%S 1,0,1,2,18,158,1788,23930,370886,6527064,128542420,2800362536,
%T 66858556196,1735834171276,48689118113374,1467253017578672,
%U 47275138863637080,1621757692715997136,59013695834307968254,2270400832166224741596,92078072790064946096284
%N Number of labeled digraphs with n arcs for which every vertex has indegree at least one and outdegree at least one.
%H Nathaniel Johnston, <a href="/A121933/b121933.txt">Table of n, a(n) for n = 0..60</a>
%F G.f.: Sum(Sum((-1)^(n-k)*binomial(n,k)*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(n-k),k=0..n),n=0..infinity).
%F a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.0722246614111436... . - _Vaclav Kotesovec_, May 07 2014
%F In closed form, c = 1/(sqrt(Pi*(1-log(2))) * log(2) * 2^(4+log(2)/2)). - _Vaclav Kotesovec_, May 04 2015
%p n:=20: t:=taylor(sum(sum((-1)^(m-k)*binomial(m,k)*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(m-k),k=0..m),m=0..n),x,n+1): seq(coeff(t,x,m),m=0..n); # _Nathaniel Johnston_, Apr 28 2011
%t Flatten[{1,Rest[CoefficientList[Series[Sum[Sum[(-1)^(n-k)*Binomial[n,k]*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(n-k),{k,0,n}],{n,1,20}],{x,0,20}],x]]}] (* _Vaclav Kotesovec_, May 07 2014 *)
%Y Cf. A121252, A086193 (by # of nodes), A367500 (unlabeled version).
%K easy,nonn
%O 0,4
%A _Vladeta Jovovic_, Sep 02 2006
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