cp's OEIS Frontend

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

%I A215858 #8 Dec 04 2014 06:57:56
%S A215858 1,36,1110,31680,904299,26603148,821278744,26864874465,935625630797,
%T A215858 34750489933016,1375999952017938,57998361908305494,
%U A215858 2596646585329104847,123180358220543885268,6175880603945440333627,326438846760992348696038,18147404450341079958539275
%N A215858 Number of simple labeled graphs on n nodes with exactly 8 connected components that are trees or cycles.
%H A215858 Alois P. Heinz, <a href="/A215858/b215858.txt">Table of n, a(n) for n = 8..150</a>
%e A215858 a(9) = 36: each graph has one 2-node tree and 7 1-node trees and C(9,2) = 36.
%p A215858 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p A215858       `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p A215858       `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p A215858     end:
%p A215858 a:= n-> T(n, 8):
%p A215858 seq(a(n), n=8..25);
%Y A215858 Column k=8 of A215861.
%Y A215858 The unlabeled version is A215988.
%K A215858 nonn
%O A215858 8,2
%A A215858 _Alois P. Heinz_, Aug 26 2012