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

1,1

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

Table of n, a(n) for n=1..16.

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

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 *)

Prog

(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), ", "))

Crossrefs

Cf. A266519.

Sequence in context: A335176 A307185 A206500 * A241705 A015475 A197947

Adjacent sequences: A266517 A266518 A266519 * A266521 A266522 A266523

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2015

Status

approved