cp's OEIS Frontend

A215857 Number of simple labeled graphs on n nodes with exactly 7 connected components that are trees or cycles.

%I A215857 #8 Dec 04 2014 06:56:40
%S A215857 1,28,714,17220,424809,11002068,303874714,9016296289,288135739892,
%T A215857 9913826194272,366486926833846,14513217676764534,613646633464214863,
%U A215857 27609928896732666760,1317652578222779606269,66497975770225498765728,3538905411811229060814213
%N A215857 Number of simple labeled graphs on n nodes with exactly 7 connected components that are trees or cycles.
%H A215857 Alois P. Heinz, <a href="/A215857/b215857.txt">Table of n, a(n) for n = 7..145</a>
%e A215857 a(8) = 28: each graph has one 2-node tree and 6 1-node trees and C(8,2) = 28.
%p A215857 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p A215857       `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p A215857       `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p A215857     end:
%p A215857 a:= n-> T(n, 7):
%p A215857 seq(a(n), n=7..25);
%Y A215857 Column k=7 of A215861.
%Y A215857 The unlabeled version is A215987.
%K A215857 nonn
%O A215857 7,2
%A A215857 _Alois P. Heinz_, Aug 26 2012