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A003514 Number of series-reduced labeled graphs with n nodes.
(Formerly M1290)
18
1, 1, 2, 4, 15, 102, 4166, 402631, 76374899, 27231987762, 18177070202320, 22801993267433275, 54212469444212172845, 246812697326518127351384, 2173787304796735262709419350, 37373588848096468764431235680525 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Cf. A003515.

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.

D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286.

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

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!.

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-Fran├žois Alcover, Nov 25 2011, after Vladeta Jovovic *)

CROSSREFS

Cf. A003515 (connected).

Row sums of A307806.

Sequence in context: A307085 A228934 A120490 * A065598 A264832 A100528

Adjacent sequences:  A003511 A003512 A003513 * A003515 A003516 A003517

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

E.g.f. and more terms from Vladeta Jovovic, Mar 23 2001

STATUS

approved

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Last modified November 20 23:06 EST 2019. Contains 329348 sequences. (Running on oeis4.)