A215859 Number of simple labeled graphs on n nodes with exactly 9 connected components that are trees or cycles.

1, 45, 1650, 54945, 1795794, 59546487, 2043490735, 73415619420, 2779264615127, 111226656560877, 4710924208619304, 211105699482022215, 9997623229700175712, 499562336689773070263, 26288415481415803589236, 1454007169289989503463230, 84361156450441837460650255

Offset: 9

Author

Alois P. Heinz, Aug 26 2012

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..150

Crossrefs

Column k=9 of A215861.

The unlabeled version is A215989.

Programs

Maple

T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
      `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
      `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
    end:
a:= n-> T(n, 9):
seq(a(n), n=9..25);