A266520 E.g.f.: log( Sum_{n>=0} (n+1)^(2*n) * x^n/n! ).

4, 65, 3252, 319422, 51147492, 12057585792, 3922351554132, 1682965461982320, 921043932965502660, 626381920753520549760, 518386843395242486312436, 513135100084662037473481728, 598802670522558079363471420836, 813678320999818358850938259419136, 1273853548265201707125719549854268820, 2276462439285471707026207820594795624448

Offset: 1

Author

Paul D. Hanna, Dec 31 2015

Keywords

• nonn

Comments

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

Links

• P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; page 139.

Crossrefs

Cf. A266519.

Programs

Mathematica

nn = 10; g[x_] := Sum[(n + 1)^(2 n) x^n/n!, {n, 0, nn}] ;
Drop[Range[0, nn]! CoefficientList[Series[Log[g[x]], {x, 0, nn}], x], 1] (* Geoffrey Critzer, Dec 06 2021 *)

PARI

{a(n) = n! * polcoeff( log( sum(m=0,n, (m+1)^(2*m) * x^m/m!) +x*O(x^n)), n)}
for(n=1,20,print1(a(n),", "))