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A058878 Triangle T(n,k) = number of labeled graphs of even degree with n nodes and k edges (n >= 0, 0<=k<=n(n-1)/2). 0
1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 4, 3, 0, 0, 1, 0, 0, 10, 15, 12, 15, 10, 0, 0, 1, 1, 0, 0, 20, 45, 72, 160, 240, 195, 120, 96, 60, 15, 0, 0, 0, 1, 0, 0, 35, 105, 252, 805, 1935, 3255, 4515, 5481, 5481, 4515, 3255, 1935, 805, 252, 105, 35, 0, 0, 1, 1, 0, 0, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 13, (1.4.7).

LINKS

Table of n, a(n) for n=0..69.

EXAMPLE

Triangle begins:

1;

1,0;

1,0,0;

1,0,0,1;

1,0,0,4,3,0,0;

...

MAPLE

w := p->expand(simplify(2^(-p)*(1+x)^(p*(p-1)/2)*add(binomial(p, n)*( (1-x)/(1+x))^(n*(p-n)), n=0..p))); T := (n, k)->coeff(w(n), x, k);

MATHEMATICA

w[p_] := 2^-p*(1+x)^(p*(p-1)/2)*Sum[Binomial[p, n]*((1-x)/(1+x))^(n*(p-n)), {n, 0, p}]; T[n_, k_] := SeriesCoefficient[w[n], {x, 0, k}]; T[0, 0] = T[1, 0] = 1; T[1, 1] = 0; Table[T[n, k], {n, 0, 8}, {k, 0, If[n<3, n, n(n-1)/2]}] // Flatten (* Jean-Fran├žois Alcover, Jan 12 2015, translated from Maple *)

CROSSREFS

Sequence in context: A284947 A261099 A030120 * A236289 A257536 A019983

Adjacent sequences:  A058875 A058876 A058877 * A058879 A058880 A058881

KEYWORD

nonn,easy,nice,tabf

AUTHOR

N. J. A. Sloane, Jan 07 2001

STATUS

approved

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Last modified November 18 17:49 EST 2018. Contains 317323 sequences. (Running on oeis4.)