cp's OEIS Frontend

A003514 Number of series-reduced labeled graphs with n nodes.

%I A003514 M1290 #40 Feb 24 2024 04:32:13
%S A003514 1,1,2,4,15,102,4166,402631,76374899,27231987762,18177070202320,
%T A003514 22801993267433275,54212469444212172845,246812697326518127351384,
%U A003514 2173787304796735262709419350,37373588848096468764431235680525,1263513534110606141026676778422031561
%N A003514 Number of series-reduced labeled graphs with n nodes.
%D A003514 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
%D A003514 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003514 Vincenzo Librandi, <a href="/A003514/b003514.txt">Table of n, a(n) for n = 0..80</a>
%H A003514 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 A003514 E.g.f.: (1 + x)^( - 1/2) * exp(x/2 - x^2/4) * Sum_{k=0..inf} (2 * exp( - x/(1 + x)))^binomial(k, 2) * (exp(x^2/2/(1 + x)))^k * x^k/k!. - _Vladeta Jovovic_, Mar 23 2001
%t A003514 max = 15; f[x_] := (1 + x)^(-1/2)*Exp[x/2-x^2/4]*Sum[(2*Exp[-x/(1+x)])^Binomial[k, 2]*Exp[x^2/2/(1+x)]^k*x^k/k!, {k, 0, max}]; CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]!(* _Jean-François Alcover_, Nov 25 2011, after Vladeta Jovovic *)
%o A003514 (PARI) seq(n)={my(x='x+O('x^(n+1))); Vec(serlaplace((1 + x)^( - 1/2) * exp(x/2 - x^2/4) * sum(k=0, n, (2 * exp(-x/(1 + x)))^binomial(k, 2) * (exp(x^2/2/(1 + x)))^k * x^k/k!)))} \\ _Andrew Howroyd_, Feb 23 2024
%Y A003514 Row sums of A060514 and A307806.
%Y A003514 The unlabeled version is A005637.
%Y A003514 Cf. A003515 (connected).
%K A003514 nonn,nice
%O A003514 0,3
%A A003514 _N. J. A. Sloane_
%E A003514 More terms from _Vladeta Jovovic_, Mar 23 2001