A215859 - OEIS

%I #8 Dec 04 2014 06:59:16

%S 1,45,1650,54945,1795794,59546487,2043490735,73415619420,

%T 2779264615127,111226656560877,4710924208619304,211105699482022215,

%U 9997623229700175712,499562336689773070263,26288415481415803589236,1454007169289989503463230,84361156450441837460650255

%N Number of simple labeled graphs on n nodes with exactly 9 connected components that are trees or cycles.

%H Alois P. Heinz, <a href="/A215859/b215859.txt">Table of n, a(n) for n = 9..150</a>

%e a(10) = 45: each graph has one 2-node tree and 8 1-node trees and C(10,2) = 45.

%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, 9):

%p seq(a(n), n=9..25);

%Y Column k=9 of A215861.

%Y The unlabeled version is A215989.

%K nonn

%O 9,2

%A _Alois P. Heinz_, Aug 26 2012