cp's OEIS Frontend

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

%I A092430 #15 Apr 29 2019 16:37:39
%S A092430 1,1,25,438,18388,1409674,206682994,58152537184,31715884061624,
%T A092430 33827568738189576,71066571962396085656,295645506683051376527648,
%U A092430 2444503529745123474354656720,40269655263141217619453414445968
%N A092430 Number of n-node labeled connected mating graphs, cf. A006024.
%C A092430 Number of n-node unlabeled connected mating graphs = number of n-node unlabeled connected graphs without endpoints, n>2; cf. A004108.
%C A092430 The number of graphs of this type with n>=1 nodes and 1<=k<=n components defines the triangle
%C A092430 0;
%C A092430 1,0;
%C A092430 1,0,0;
%C A092430 25,3,0,0;
%C A092430 438,10,0,0,0;
%C A092430 18388,385,15,0,0,0;
%C A092430 1409674,10073,105,0,0,0,0;
%C A092430 206682994,561267,5530,105,0,0,0,0;
%C A092430 58152537184,53672556,197344,1260,0,0,0,0,0;
%C A092430 with row sums A007833. - _R. J. Mathar_, Apr 29 2019
%D A092430 Goran Kilibarda, "Enumeration of unlabeled mating graphs", Belgrade, 2004, to be published.
%H A092430 Andrew Howroyd, <a href="/A092430/b092430.txt">Table of n, a(n) for n = 2..50</a>
%H A092430 Goran Kilibarda, <a href="http://www.springerlink.com/content/e1m13421h2873t62/">Enumeration of Unlabeled Mating Graphs</a>, Graphs and Combinatorics, Volume 23, Number 2 / April, 2007, pp. 183-199.
%F A092430 From _Vladeta Jovovic_, Mar 28 2004: (Start)
%F A092430 E.g.f.: log((Sum_{n>=0} 2^binomial(n, 2)*log(1+x)^n/n!)/(1+x)).
%F A092430 a(n) = A079306(n) + (-1)^n*(n-1)!. (End)
%o A092430 (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
%Y A092430 Cf. A006024, A079306, A007833, A004108.
%Y A092430 Cf. A059166.
%K A092430 nonn
%O A092430 2,3
%A A092430 Goran Kilibarda, _Vladeta Jovovic_, Mar 22 2004