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

9,2

Links

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

Example

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

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);

Crossrefs

Column k=9 of A215861.

The unlabeled version is A215989.

Sequence in context: A014940 A273436 A049397 * A143170 A328351 A203828

Adjacent sequences: A215856 A215857 A215858 * A215860 A215861 A215862

Keyword

nonn

Author

Alois P. Heinz, Aug 26 2012

Status

approved