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

10,2

Links

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

Example

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

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);

Crossrefs

Column k=10 of A215861.

The unlabeled version is A215980.

Sequence in context: A240687 A053113 A012048 * A020536 A212788 A131557

Adjacent sequences: A215857 A215858 A215859 * A215861 A215862 A215863

Keyword

nonn

Author

Alois P. Heinz, Aug 26 2012

Status

approved