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

Author

Alois P. Heinz, Aug 25 2012

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column k=5 of A215861.

The unlabeled version is A215985.

Programs

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);