OFFSET
0,3
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..80
D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286.
FORMULA
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Mar 23 2001
STATUS
approved