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A215855 Number of simple labeled graphs on n nodes with exactly 5 connected components that are trees or cycles.

%I A215855 #10 Dec 04 2014 06:55:00
%S A215855 1,15,245,3990,70707,1381695,30015205,724574235,19353600409,
%T A215855 568456078190,18238727824135,635132015698180,23864603640853943,
%U A215855 962474842863397305,41472195692307932196,1901422216588179732355,92422276780875117660486,4747285506511684927770980
%N A215855 Number of simple labeled graphs on n nodes with exactly 5 connected components that are trees or cycles.
%H A215855 Alois P. Heinz, <a href="/A215855/b215855.txt">Table of n, a(n) for n = 5..145</a>
%e A215855 a(6) = 15: each graph has one 2-node tree and 4 1-node trees, and C(6,2) = 15.
%p A215855 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p A215855       `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p A215855       `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p A215855     end:
%p A215855 a:= n-> T(n, 5):
%p A215855 seq(a(n), n=5..25);
%Y A215855 Column k=5 of A215861.
%Y A215855 The unlabeled version is A215985.
%K A215855 nonn
%O A215855 5,2
%A A215855 _Alois P. Heinz_, Aug 25 2012