cp's OEIS Frontend

A215774 Number of undirected labeled graphs on n+4 nodes with exactly n cycle graphs as connected components.

%I A215774 #11 Apr 30 2015 20:31:03
%S A215774 0,12,127,742,3157,10857,31899,82929,195459,425139,864864,1662661,
%T A215774 3045406,5349526,9059946,14858646,23684298,36804558,55902693,83180328,
%U A215774 121478203,174416935,246559885,343600335,472575285,642108285,862683822,1146955887,1510093452
%N A215774 Number of undirected labeled graphs on n+4 nodes with exactly n cycle graphs as connected components.
%H A215774 Alois P. Heinz, <a href="/A215774/b215774.txt">Table of n, a(n) for n = 0..1000</a>
%F A215774 G.f.: (43*x^3+31*x^2+19*x+12)*x/(1-x)^9.
%F A215774 a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(15*n^3+30*n^2+245*n+286)/5760.
%e A215774 a(1) = 12 = 4!/2: (1-2-3-4-5-1), (1-2-3-5-4-1), (1-2-4-3-5-1), (1-2-4-5-3-1), (1-2-5-3-4-1), (1-2-5-4-3-1), (1-3-2-4-5-1), (1-3-2-5-4-1), (1-3-4-2-5-1), (1-3-5-2-4-1), (1-4-2-3-5-1), (1-4-3-2-5-1).
%p A215774 a:= n-> (6864+(20180+(22980+(13295+(4536+(1070+(180+15*n)*
%p A215774                n)*n)*n)*n)*n)*n)*n/5760:
%p A215774 seq(a(n), n=0..40);
%Y A215774 A diagonal of A215771.
%K A215774 nonn
%O A215774 0,2
%A A215774 _Alois P. Heinz_, Aug 23 2012