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%I #10 Nov 08 2019 09:47:35
%S 0,2,20,600,70048,34265920,69135737856,563921434969088,
%T 18455775305195147264,2418183926567027902291968,
%U 1267698967252460350153517105152,2658483881480146168943131337243754496,22300809002478630462447974400280680553512960
%N The number of connected components in all labeled directed graphs (with self loops allowed) on n nodes.
%H Andrew Howroyd, <a href="/A197743/b197743.txt">Table of n, a(n) for n = 0..50</a>
%F E.g.f.: B(A(x)) where A(x) = log(Sum_{k=1..n} 2^(n^2)x^n/n!) and B(x)= x*exp(x).
%F a(n) = Sum_{k=1..n} k*A186236(n,k).
%t a=Sum[2^(n^2)x^n/n!, {n,0,20}]; Range[0,20]! CoefficientList[Series[a Log[a], {x,0,20}], x]
%o (PARI) seq(n)={my(g=log(sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n))); Vec(serlaplace(g*exp(g)), -(n+1))} \\ _Andrew Howroyd_, Nov 07 2019
%Y Cf. A062738, A186236.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Oct 17 2011
%E Terms a(11) and beyond from _Andrew Howroyd_, Nov 07 2019
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