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.

A217652 Number of isolated nodes over all labeled directed graphs on n nodes.

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%I A217652 #23 Nov 13 2012 09:38:00
%S A217652 0,1,2,12,256,20480,6291456,7516192768,35184372088832,
%T A217652 648518346341351424,47223664828696452136960,
%U A217652 13617340432139183023890366464,15576890575604482885591488987660288,70778732319555200400381918345807787982848
%N A217652 Number of isolated nodes over all labeled directed graphs on n nodes.
%C A217652 a(n) = Sum_{k=1..n} A217580(n,k) * k.
%C A217652 a(n) is also the number of labeled directed graphs on n nodes with an "Emperor". - _Rémy-Robert Joseph_, Nov 12 2012
%H A217652 Alois P. Heinz, <a href="/A217652/b217652.txt">Table of n, a(n) for n = 0..40</a>
%F A217652 E.g.f.: x * A(x) where A(x) is the e.g.f. for A053763.
%F A217652 a(n) = 2^(n^2-3*n+2)*n. - _Alois P. Heinz_, Oct 09 2012
%p A217652 a:= n-> 2^(n^2-3*n+2)*n:
%p A217652 seq (a(n), n=0..15);  # _Alois P. Heinz_, Oct 09 2012
%t A217652 nn=15; s=Sum[2^(n^2-n)x^n/n!,{n,0,nn}]; Range[0,nn]! CoefficientList[Series[x s, {x,0,nn}], x]
%o A217652 (Maxima) A217652(n):=2^(n^2-3*n+2)*n$ makelist(A217652(n),n,0,10); /* _Martin Ettl_, Nov 13 2012 */
%Y A217652 See also A123903 (case of tournaments) and A219116 (case of semicomplete digraphs) _Rémy-Robert Joseph_, Nov 12 2012
%K A217652 nonn
%O A217652 0,3
%A A217652 _Geoffrey Critzer_, Oct 09 2012