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A215855 Number of simple labeled graphs on n nodes with exactly 5 connected components that are trees or cycles. 3

%I

%S 1,15,245,3990,70707,1381695,30015205,724574235,19353600409,

%T 568456078190,18238727824135,635132015698180,23864603640853943,

%U 962474842863397305,41472195692307932196,1901422216588179732355,92422276780875117660486,4747285506511684927770980

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

%H Alois P. Heinz, <a href="/A215855/b215855.txt">Table of n, a(n) for n = 5..145</a>

%e a(6) = 15: each graph has one 2-node tree and 4 1-node trees, and C(6,2) = 15.

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

%p `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*

%p `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))

%p end:

%p a:= n-> T(n, 5):

%p seq(a(n), n=5..25);

%Y Column k=5 of A215861.

%Y The unlabeled version is A215985.

%K nonn

%O 5,2

%A _Alois P. Heinz_, Aug 25 2012

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Last modified March 28 10:27 EDT 2020. Contains 333082 sequences. (Running on oeis4.)