Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Nov 07 2019 19:24:04
%S 1,0,3,54,3861,1028700,1067510583,4390552197234,72022439672173161,
%T 4721718122762915558520,1237892818862615769794806443,
%U 1298060597552993036455274183624814,5444502293926142814638982021027945429501,91343781554550362267223855965291602454111295060
%N Number of labeled digraphs on n unisolated nodes (inverse binomial transform of A053763).
%H Andrew Howroyd, <a href="/A054545/b054545.txt">Table of n, a(n) for n = 0..50</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)).
%e 2^(n*(n-1))=1+3*C(n,2)+54*C(n,3)+3861*C(n,4)+...
%t 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 *)
%o (PARI) a(n)={sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)))} \\ _Andrew Howroyd_, Nov 07 2019
%Y Cf. A006129.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Apr 09 2000
%E Terms a(12) and beyond from _Andrew Howroyd_, Nov 07 2019