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%I #7 May 10 2013 12:44:44
%S 1,6,19,68,242,704,1981,5140,12364,27614,57598,113108,210812,375606,
%T 643646,1066196,1714445,2685464,4109493,6158768,9058119,13097592,
%U 18647371,26175300,36267330,49651242,67224024,90083308,119563302
%N Number of homeomorphically irreducible general graphs on 4 labeled nodes and with n edges.
%C A homeomorphically irreducible general graph is a graph with multiple edges and loops and without nodes of degree 2.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983.
%H V. Jovovic, <a href="/A060576/a060576.pdf">Generating functions for homeomorphically irreducible general graphs on n labeled nodes</a>
%H V. Jovovic, <a href="/A060576/a060576_rec.pdf">Recurrences for the numbers of homeomorphically irreducible general graphs on m labeled nodes and n edges</a>
%F G.f.: (4*x^15 + 5*x^14 - 194*x^13 + 881*x^12 - 2058*x^11 + 3096*x^10 - 3330*x^9 + 2628*x^8 - 1398*x^7 + 359*x^6 + 72*x^5 - 93*x^4 + 28*x^3 + 4*x^2 - 4*x + 1)/(x - 1)^10. E.g.f. for homeomorphically irreducible general graphs with n nodes and k edges is (1 + x*y)^( - 1/2)*exp( - x*y/2 + x^2*y^2/4)*Sum_{k >= 0} 1/(1 - x)^binomial(k + 1, 2)*exp( - x^2*y*k^2/(2*(1 + x*y)) - x^2*y*k/2)*y^k/k!.
%Y Cf. A003514, A060516, A060533-A060537, A060576-A060581.
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, Apr 03 2001
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