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A215764 Number of undirected labeled graphs on n nodes with exactly 4 cycle graphs as connected components.

%I A215764 #6 Aug 23 2012 21:06:08
%S A215764 1,10,65,420,3157,27342,264925,2831455,33077539,419262987,5730379473,
%T A215764 84009491475,1315019717433,21890336017248,386143234692768,
%U A215764 7195289865439824,141228388872794736,2912462945497687680,62959048637195335680,1423638554827333204800
%N A215764 Number of undirected labeled graphs on n nodes with exactly 4 cycle graphs as connected components.
%H A215764 Alois P. Heinz, <a href="/A215764/b215764.txt">Table of n, a(n) for n = 4..175</a>
%e A215764 a(4) = 1:  o1.2o
%e A215764 .          .....
%e A215764 .          o3.4o
%p A215764 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1,
%p A215764       add(binomial(n-1, i)*T(n-1-i, k-1)*ceil(i!/2), i=0..n-k)))
%p A215764     end:
%p A215764 a:= n-> T(n, 4):
%p A215764 seq (a(n), n=4..25);
%Y A215764 Column k=4 of A215771.
%K A215764 nonn
%O A215764 4,2
%A A215764 _Alois P. Heinz_, Aug 23 2012