A215855 Number of simple labeled graphs on n nodes with exactly 5 connected components that are trees or cycles.

1, 15, 245, 3990, 70707, 1381695, 30015205, 724574235, 19353600409, 568456078190, 18238727824135, 635132015698180, 23864603640853943, 962474842863397305, 41472195692307932196, 1901422216588179732355, 92422276780875117660486, 4747285506511684927770980

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..145

Example

a(6) = 15: each graph has one 2-node tree and 4 1-node trees, and C(6,2) = 15.

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, 5):
seq(a(n), n=5..25);

Crossrefs

Column k=5 of A215861.

The unlabeled version is A215985.

Sequence in context: A133199 A059760 A059615 * A163031 A065920 A273624

Adjacent sequences: A215852 A215853 A215854 * A215856 A215857 A215858

Keyword

nonn

Author

Alois P. Heinz, Aug 25 2012

Status

approved