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%I #16 Dec 08 2021 08:56:44
%S 4,65,3252,319422,51147492,12057585792,3922351554132,1682965461982320,
%T 921043932965502660,626381920753520549760,518386843395242486312436,
%U 513135100084662037473481728,598802670522558079363471420836,813678320999818358850938259419136,1273853548265201707125719549854268820,2276462439285471707026207820594795624448
%N E.g.f.: Log( Sum_{n>=0} (n+1)^(2*n) * x^n/n! ).
%C From two partial functions f,g on [n], form a labeled directed graph with vertex set [n] and edge set: {(x -> f(x)):x in [n]} Union {{(x -> g(x)):x in [n]}. Then a(n) is the number of such graphs that are weakly connected. - _Geoffrey Critzer_, Dec 06 2021
%H P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; page 139.
%t nn = 10; g[x_] := Sum[(n + 1)^(2 n) x^n/n!, {n, 0, nn}] ;
%t Drop[Range[0, nn]! CoefficientList[Series[Log[g[x]], {x, 0, nn}], x], 1] (* _Geoffrey Critzer_, Dec 06 2021 *)
%o (PARI) {a(n) = n! * polcoeff( log( sum(m=0,n, (m+1)^(2*m) * x^m/m!) +x*O(x^n)), n)}
%o for(n=1,20,print1(a(n),", "))
%Y Cf. A266519.
%K nonn
%O 1,1
%A _Paul D. Hanna_, Dec 31 2015
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