cp's OEIS Frontend

A215856 Number of simple labeled graphs on n nodes with exactly 6 connected components that are trees or cycles.

%I A215856 #9 Dec 04 2014 06:56:06
%S A215856 1,21,434,8694,183099,4138827,101682724,2726328033,79746709042,
%T A215856 2537322057270,87447979819018,3249640607490732,129613729260208069,
%U A215856 5525005710150786189,250709547490889697735,12067446246711780717009,614138343777115783675203
%N A215856 Number of simple labeled graphs on n nodes with exactly 6 connected components that are trees or cycles.
%H A215856 Alois P. Heinz, <a href="/A215856/b215856.txt">Table of n, a(n) for n = 6..145</a>
%e A215856 a(7) = 21: each graph has one 2-node tree and 5 1-node trees and C(7,2) = 21.
%p A215856 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p A215856       `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p A215856       `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p A215856     end:
%p A215856 a:= n-> T(n, 6):
%p A215856 seq(a(n), n=6..25);
%Y A215856 Column k=6 of A215861.
%Y A215856 The unlabeled version is A215986.
%K A215856 nonn
%O A215856 6,2
%A A215856 _Alois P. Heinz_, Aug 26 2012