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%I #26 Jan 24 2020 19:15:53
%S 1,1,0,4,5,96,548,7908,84696,1331840,20255774,372819387,7170089146,
%T 154824436840,3558826861734,88938133663711,2367074592366594,
%U 67402755251544804,2034875403034891874,65102692993820702700,2196725886835707259041,78036983096041464230268
%N Number of series-reduced connected labeled graphs with n edges.
%C Series-reduced graphs are also called homeomorphically irreducible graphs and are the graphs without vertices of degree 2.
%H Andrew Howroyd, <a href="/A331584/b331584.txt">Table of n, a(n) for n = 0..100</a>
%H D. M. Jackson and J. W. Reilly, <a href="https://doi.org/10.1016/0095-8956(75)90090-8">The enumeration of homeomorphically irreducible labeled graphs</a>, J. Combin. Theory, B 19 (1975), 272-286.
%o (PARI) \\ See Jackson & Reilly link for e.g.f.
%o H(n,y) = {my(A=O(x*x^n)); (exp(y*x/2 - (y*x)^2/4 + A)/sqrt(1 + y*x + A))*sum(k=0, n, ((1 + y)*exp(-y^2*x/(1+y*x) + A))^binomial(k,2) * (x*exp((y^3*x^2 + A)/(2*(1 + y*x))))^k / k!)}
%o seq(n)={Vec(subst(Pol(serlaplace(log(H(n, y+O(y^n))))), x, 1))}
%Y Row sums of A331437.
%Y Column sums of A331438.
%Y Cf. A003515.
%K nonn
%O 0,4
%A _Andrew Howroyd_, Jan 24 2020