A215854 Number of simple labeled graphs on n nodes with exactly 4 connected components that are trees or cycles.

1, 10, 125, 1610, 23597, 394506, 7533445, 163190665, 3971678359, 107502644249, 3205669601953, 104435680520535, 3690517248021753, 140590728463023632, 5743180320999041664, 250423270549658253350, 11608409727652016747176, 570034426072900362961212

Offset: 4

Author

Alois P. Heinz, Aug 25 2012

Keywords

• nonn

Examples

			a(4) = 1: the graph with 4 1-node trees.
a(5) = 10: each graph has one 2-node tree and 3 1-node trees, and C(5,2) = 10.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..145

Crossrefs

Column k=4 of A215861.

The unlabeled version is A215984.

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, 4):
seq(a(n), n=4..25);