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 A215854 Number of simple labeled graphs on n nodes with exactly 4 connected components that are trees or cycles. 3

%I

%S 1,10,125,1610,23597,394506,7533445,163190665,3971678359,107502644249,

%T 3205669601953,104435680520535,3690517248021753,140590728463023632,

%U 5743180320999041664,250423270549658253350,11608409727652016747176,570034426072900362961212

%N Number of simple labeled graphs on n nodes with exactly 4 connected components that are trees or cycles.

%H Alois P. Heinz, <a href="/A215854/b215854.txt">Table of n, a(n) for n = 4..145</a>

%e a(4) = 1: the graph with 4 1-node trees.

%e a(5) = 10: each graph has one 2-node tree and 3 1-node trees, and C(5,2) = 10.

%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, 4):

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

%Y Column k=4 of A215861.

%Y The unlabeled version is A215984.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Aug 25 2012

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)