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%I #32 Apr 03 2023 15:15:17
%S 0,1,4,48,2048,327680,201326592,481036337152,4503599627370496,
%T 166020696663385964544,24178516392292583494123520,
%U 13944156602510523416463735259136,31901471898837980949691369446728269824,289909687580898100839964337544428699577745408
%N The number of isolated nodes in all labeled directed graphs (with self loops allowed) on n nodes.
%C Here, isolated means indegree = outdegree = 0.
%C a(n) is also the number of directed graphs on [n] (no self loops allowed, A053763) with a distinguished vertex of indegree 0. - _Geoffrey Critzer_, Apr 01 2023
%F E.g.f.: x*A(x) where A(x) = Sum_{n>=0} 2^(n^2)*x^n/n!.
%F a(n) = n * 2^((n-1)^2) = n*A002416(n-1).
%F Sum_{n>=0} a(n)*z^n/B(n) = z*Sum_{n>=0} A053763(n)*z^n/B(n) where B(n) = n!*2^binomial(n,2). - _Geoffrey Critzer_, Apr 01 2023
%t a = Sum[2^(n^2)x^n/n!, {n,0,20}]; Range[0,12]! CoefficientList[Series[x a, {x,0,12}], x]
%Y Cf. A011266, A053763, A002416.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Oct 19 2011
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