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

6,2

Links

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

Example

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

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);

Crossrefs

Column k=6 of A215861.

The unlabeled version is A215986.

Sequence in context: A064108 A353144 A067895 * A297692 A218840 A171326

Adjacent sequences: A215853 A215854 A215855 * A215857 A215858 A215859

Keyword

nonn

Author

Alois P. Heinz, Aug 26 2012

Status

approved