A014501 - OEIS

%I #28 Jan 13 2020 13:53:52

%S 1,2,7,43,403,5245,89132,1898630,49209846,1517275859,54669946851,

%T 2269075206395,107199678164289,5707320919486026,339510756324234931,

%U 22400182888853554291,1628654713107465602783,129754625253841669625051

%N Number of graphs with loops, having unlabeled (non-isolated) nodes and n labeled edges.

%D G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

%H Andrew Howroyd, <a href="/A014501/b014501.txt">Table of n, a(n) for n = 0..200</a>

%H 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 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 E.g.f.: exp(-1+x/2)*Sum((1+x)^binomial(n+1, 2)/n!, n=0..infinity) [probably in the Labelle paper]. - _Vladeta Jovovic_, Apr 27 2004

%Y Row n=2 of A331161.

%Y Cf. A020554, A020555, A014500.

%K nonn

%O 0,2

%A _Simon Plouffe_, Gilbert Labelle (gilbert(AT)lacim.uqam.ca).