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Number of undirected labeled graphs on n nodes with exactly 4 cycle graphs as connected components.
2

%I #6 Aug 23 2012 21:06:08

%S 1,10,65,420,3157,27342,264925,2831455,33077539,419262987,5730379473,

%T 84009491475,1315019717433,21890336017248,386143234692768,

%U 7195289865439824,141228388872794736,2912462945497687680,62959048637195335680,1423638554827333204800

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

%H Alois P. Heinz, <a href="/A215764/b215764.txt">Table of n, a(n) for n = 4..175</a>

%e a(4) = 1: o1.2o

%e . .....

%e . o3.4o

%p T:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1,

%p add(binomial(n-1, i)*T(n-1-i, k-1)*ceil(i!/2), i=0..n-k)))

%p end:

%p a:= n-> T(n, 4):

%p seq (a(n), n=4..25);

%Y Column k=4 of A215771.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Aug 23 2012