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%I A020558 #20 Aug 09 2024 16:21:02
%S A020558 1,1,4,27,274,3874,71995,1682448,47840813,1615315141,63566760077,
%T A020558 2873099980637,147384910116793,8496500896980637,545845612016485842,
%U A020558 38797966029876716897,3032005571734589578076
%N A020558 Number of ordered multigraphs on n labeled edges (without loops).
%D A020558 G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.
%H A020558 G. Labelle, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00265-4">Counting enriched multigraphs according to the number of their edges (or arcs)</a>, Discrete Math., 217 (2000), 237-248.
%H A020558 G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]
%F A020558 E.g.f.: exp((3*x-2)/(2-2*x))*Sum(1/(n!*(1-x)^binomial(n, 2)), n = 0 .. infinity). a(n) = Sum((-1)^(n-k)*Stirling1(n, k)*A020554(k), k=0..n). - _Vladeta Jovovic_, May 02 2004
%F A020558 E.g.f.: exp(x/(2-2*x))*Sum(A020556(n)*(-log(1-x)/2)^n/n!, n=0..infinity). - _Vladeta Jovovic_, May 02 2004
%K A020558 nonn
%O A020558 0,3
%A A020558 Gilbert Labelle (gilbert(AT)lacim.uqam.ca), _Simon Plouffe_

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