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A215763 Number of undirected labeled graphs on n nodes with exactly 3 cycle graphs as connected components.

%I A215763 #9 Aug 23 2012 21:05:59
%S A215763 1,6,25,120,742,5446,45559,427275,4437279,50532669,626068404,
%T A215763 8382651732,120614527728,1855938746160,30411098170560,528670269132480,
%U A215763 9718179216603840,188342519176964160,3838144417230700800,82046606738914540800,1835772107381126208000
%N A215763 Number of undirected labeled graphs on n nodes with exactly 3 cycle graphs as connected components.
%H A215763 Alois P. Heinz, <a href="/A215763/b215763.txt">Table of n, a(n) for n = 3..175</a>
%e A215763 a(4) = 6:  .1.2o  .1-2.  o1.2.  o1.2o  o1.2.  .1.2o
%e A215763 .          .|...  .....  ...|.  .....  ../..  ..\..
%e A215763 .          .3.4o  o3.4o  o3.4.  .3-4.  .3.4o  o3.4.
%p A215763 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0, `if`(n=0, 1,
%p A215763       add(binomial(n-1, i)*T(n-1-i, k-1)*ceil(i!/2), i=0..n-k)))
%p A215763     end:
%p A215763 a:= n-> T(n, 3):
%p A215763 seq (a(n), n=3..25);
%Y A215763 Column k=3 of A215771.
%K A215763 nonn
%O A215763 3,2
%A A215763 _Alois P. Heinz_, Aug 23 2012