A215858 Number of simple labeled graphs on n nodes with exactly 8 connected components that are trees or cycles.

1, 36, 1110, 31680, 904299, 26603148, 821278744, 26864874465, 935625630797, 34750489933016, 1375999952017938, 57998361908305494, 2596646585329104847, 123180358220543885268, 6175880603945440333627, 326438846760992348696038, 18147404450341079958539275

Offset: 8

Author

Alois P. Heinz, Aug 26 2012

Keywords

• nonn

Examples

			a(9) = 36: each graph has one 2-node tree and 7 1-node trees and C(9,2) = 36.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..150

Crossrefs

Column k=8 of A215861.

The unlabeled version is A215988.

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, 8):
seq(a(n), n=8..25);