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A215858 Number of simple labeled graphs on n nodes with exactly 8 connected components that are trees or cycles. 3

%I #8 Dec 04 2014 06:57:56

%S 1,36,1110,31680,904299,26603148,821278744,26864874465,935625630797,

%T 34750489933016,1375999952017938,57998361908305494,

%U 2596646585329104847,123180358220543885268,6175880603945440333627,326438846760992348696038,18147404450341079958539275

%N Number of simple labeled graphs on n nodes with exactly 8 connected components that are trees or cycles.

%H Alois P. Heinz, <a href="/A215858/b215858.txt">Table of n, a(n) for n = 8..150</a>

%e a(9) = 36: each graph has one 2-node tree and 7 1-node trees and C(9,2) = 36.

%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, 8):

%p seq(a(n), n=8..25);

%Y Column k=8 of A215861.

%Y The unlabeled version is A215988.

%K nonn

%O 8,2

%A _Alois P. Heinz_, Aug 26 2012

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)