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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.
2
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
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
Sequence in context: A302288 A149490 A304977 * A329777 A323787 A132837
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 12 2008
STATUS
approved