A143406 Number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains a nonempty set of labels of equal size, also row sums of A143398.

1, 1, 4, 14, 55, 252, 1319, 7737, 50040, 351636, 2659375, 21519027, 185279186, 1688183135, 16206401020, 163376811610, 1724624368377, 19011582728772, 218312877627483, 2605840967052663, 32271957793959066, 413991491885677105, 5492584623675060620

Offset: 0

Author

Alois P. Heinz, Aug 12 2008

Keywords

• nonn

Examples

			a(2) = 4, because 4 forests with 2 labels exist: {1}{2}, {1}<-2, {2}<-1, {1,2}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..530
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A143398, A000142.

Programs

Maple

a:= n-> if n=0 then 1 else n! * add(add(i^(n-k*i)/
        ((n-k*i)!*i!*k!^i), i=1..floor(n/k)), k=1..n) fi:
seq(a(n), n=0..30);

Formula

a(n) = 1 if n=0 and a(n) = n! * Sum_{k=1..n} Sum_{i=1..floor(n/k)} i^(n-k*i)/ ((n-k*i)!*i!*k!^i) else.