A215856 Number of simple labeled graphs on n nodes with exactly 6 connected components that are trees or cycles.

1, 21, 434, 8694, 183099, 4138827, 101682724, 2726328033, 79746709042, 2537322057270, 87447979819018, 3249640607490732, 129613729260208069, 5525005710150786189, 250709547490889697735, 12067446246711780717009, 614138343777115783675203

Offset: 6

Author

Alois P. Heinz, Aug 26 2012

Keywords

• nonn

Examples

			a(7) = 21: each graph has one 2-node tree and 5 1-node trees and C(7,2) = 21.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..145

Crossrefs

Column k=6 of A215861.

The unlabeled version is A215986.

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, 6):
seq(a(n), n=6..25);