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A143406
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Number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains a non-empty set of labels of equal size, also row sums of A143398.
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2
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1, 1, 4, 14, 55, 252, 1319, 7737, 50040, 351636, 2659375, 21519027, 185279186, 1688183135, 16206401020, 163376811610, 1724624368377, 19011582728772, 218312877627483, 2605840967052663, 32271957793959066, 413991491885677105
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to rooted trees
Alois P. Heinz, Table of n, a(n) for n = 0..200
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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.
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EXAMPLE
| a(2) = 4, because 4 forests with 2 labels exist: {1}{2}, {1}<-2, {2}<-1, {1,2}.
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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);
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CROSSREFS
| Cf. A143398, A000142.
Sequence in context: A162481 A088655 A149490 * A132837 A149491 A073155
Adjacent sequences: A143403 A143404 A143405 * A143407 A143408 A143409
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KEYWORD
| nonn
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 12 2008
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