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%I M4009 #23 Jan 24 2020 19:17:07
%S 0,1,1,0,5,51,3634,374119,73161880,26545249985,17904840957826,
%T 22602069719494379,53938857227326533032,246107945479472758874483,
%U 2170331943503938546383205218,37340982087637629911717846092591,1262915556964772342158139988356979872
%N Number of series-reduced connected labeled graphs with n nodes.
%C Jackson and Reilly paper has typographical error in value for a(12). - _Sean A. Irvine_, Jun 17 2015
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrew Howroyd, <a href="/A003515/b003515.txt">Table of n, a(n) for n = 0..50</a> (terms 0..34 from Sean A. Irvine)
%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.
%F E.g.f.: log(B(x)) where B(x) is the e.g.f. for A003514. - _Sean A. Irvine_, Jun 17 2015
%o (PARI) \\ See Jackson & Reilly for e.g.f.
%o seq(n)={my(A=O(x*x^n)); Vec(serlaplace(log((exp(x/2 - x^2/4 + A)/sqrt(1 + x + A))*sum(k=0, n, (2*exp(-x/(1+x) + A))^binomial(k,2) * (x*exp((x^2 + A)/(2*(1 + x))))^k / k!))), -(n+1))} \\ _Andrew Howroyd_, Jan 24 2020
%Y Row sums of A331438.
%Y Column sums of A331437.
%Y Cf. A003514, A331584.
%K nonn
%O 0,5
%A _N. J. A. Sloane_
%E More terms and a(12) corrected by _Sean A. Irvine_, Jun 17 2015
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