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

8,2

Links

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

Example

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

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);

Crossrefs

Column k=8 of A215861.

The unlabeled version is A215988.

Sequence in context: A000809 A151584 A233085 * A103278 A004294 A378245

Adjacent sequences: A215855 A215856 A215857 * A215859 A215860 A215861

Keyword

nonn

Author

Alois P. Heinz, Aug 26 2012

Status

approved