cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A054545 #15 Nov 07 2019 19:24:04
%S A054545 1,0,3,54,3861,1028700,1067510583,4390552197234,72022439672173161,
%T A054545 4721718122762915558520,1237892818862615769794806443,
%U A054545 1298060597552993036455274183624814,5444502293926142814638982021027945429501,91343781554550362267223855965291602454111295060
%N A054545 Number of labeled digraphs on n unisolated nodes (inverse binomial transform of A053763).
%H A054545 Andrew Howroyd, <a href="/A054545/b054545.txt">Table of n, a(n) for n = 0..50</a>
%H A054545 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A054545 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)).
%e A054545 2^(n*(n-1))=1+3*C(n,2)+54*C(n,3)+3861*C(n,4)+...
%t A054545 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 A054545 (PARI) a(n)={sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)))} \\ _Andrew Howroyd_, Nov 07 2019
%Y A054545 Cf. A006129.
%K A054545 easy,nonn
%O A054545 0,3
%A A054545 _Vladeta Jovovic_, Apr 09 2000
%E A054545 Terms a(12) and beyond from _Andrew Howroyd_, Nov 07 2019