A054545 Number of labeled digraphs on n unisolated nodes (inverse binomial transform of A053763).

1, 0, 3, 54, 3861, 1028700, 1067510583, 4390552197234, 72022439672173161, 4721718122762915558520, 1237892818862615769794806443, 1298060597552993036455274183624814, 5444502293926142814638982021027945429501, 91343781554550362267223855965291602454111295060

Offset: 0

Author

Vladeta Jovovic, Apr 09 2000

Keywords

• easy
• nonn

Examples

			2^(n*(n-1))=1+3*C(n,2)+54*C(n,3)+3861*C(n,4)+...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A006129.

Programs

Mathematica

nn=20;s=Sum[2^(2Binomial[n,2])x^n/n!,{n,0,nn}];Range[0,nn]!CoefficientList[Series[ s/Exp[x],{x,0,nn}],x]  (* Geoffrey Critzer, Oct 07 2012 *)

PARI

a(n)={sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)))} \\ Andrew Howroyd, Nov 07 2019

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)).

Extensions

Terms a(12) and beyond from Andrew Howroyd, Nov 07 2019