A092430 Number of n-node labeled connected mating graphs, cf. A006024.

1, 1, 25, 438, 18388, 1409674, 206682994, 58152537184, 31715884061624, 33827568738189576, 71066571962396085656, 295645506683051376527648, 2444503529745123474354656720, 40269655263141217619453414445968

Offset: 2

Author

Goran Kilibarda, Vladeta Jovovic, Mar 22 2004

Keywords

• nonn

Comments

Number of n-node unlabeled connected mating graphs = number of n-node unlabeled connected graphs without endpoints, n>2; cf. A004108.

The number of graphs of this type with n>=1 nodes and 1<=k<=n components defines the triangle

0;

1,0;

1,0,0;

25,3,0,0;

438,10,0,0,0;

18388,385,15,0,0,0;

1409674,10073,105,0,0,0,0;

206682994,561267,5530,105,0,0,0,0;

58152537184,53672556,197344,1260,0,0,0,0,0;

with row sums A007833. - R. J. Mathar, Apr 29 2019

References

• Goran Kilibarda, "Enumeration of unlabeled mating graphs", Belgrade, 2004, to be published.

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..50
• Goran Kilibarda, Enumeration of Unlabeled Mating Graphs, Graphs and Combinatorics, Volume 23, Number 2 / April, 2007, pp. 183-199.

Crossrefs

Cf. A006024, A079306, A007833, A004108.

Cf. A059166.

Programs

PARI

a(n)={n!*polcoef(log(sum(i=0, n, 2^binomial(i, 2)*log(1+x + O(x*x^n))^i/i!)/(1+x)), n)} \\ Andrew Howroyd, Sep 09 2018

Formula

From Vladeta Jovovic, Mar 28 2004: (Start)

E.g.f.: log((Sum_{n>=0} 2^binomial(n, 2)*log(1+x)^n/n!)/(1+x)).

a(n) = A079306(n) + (-1)^n*(n-1)!. (End)