A215860 Number of simple labeled graphs on n nodes with exactly 10 connected components that are trees or cycles.

1, 55, 2365, 90805, 3367364, 124984860, 4743643190, 186488038880, 7653850266777, 329429479792985, 14903545528332565, 709243144460040645, 35495878932860944422, 1866637759375098988740, 103014318586612720480259, 5957391569989223921495400

Offset: 10

Author

Alois P. Heinz, Aug 26 2012

Keywords

• nonn

Examples

			a(11) = 55: each graph has one 2-node tree and 9 1-node trees and C(11,2) = 55.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..150

Crossrefs

Column k=10 of A215861.

The unlabeled version is A215980.

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, 10):
seq(a(n), n=10..30);