A014505 - OEIS

%I #19 Aug 09 2024 16:21:13

%S 1,1,6,68,1206,29982,981476,40515568,2044492988,123175320988,

%T 8697475219688,709097832452880,65934837808883016,6920436929999656936,

%U 812724019581549433520,105986960037601701495680

%N Number of digraphs with unlabeled (non-isolated) nodes and n labeled edges.

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

%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) * Sum_{n>=0} (1+x)^(n^2-n) / n!. - _Paul D. Hanna_, Apr 25 2018

%F a(n) = n!*exp(-1) * Sum_{k>=sqrt(n)} binomial(k^2-k, n) / k!. - _Paul D. Hanna_, Apr 25 2018

%Y Cf. A014507.

%K nonn

%O 0,3

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