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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..530

Index entries for sequences related to rooted trees

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.

Example

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

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);

Crossrefs

Cf. A143398, A000142.

Sequence in context: A302288 A149490 A304977 * A329777 A323787 A132837

Adjacent sequences: A143403 A143404 A143405 * A143407 A143408 A143409

Keyword

nonn

Author

Alois P. Heinz, Aug 12 2008

Status

approved