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A143405
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Number of forests of labeled rooted trees of height at most 1, with n labels, where any root may contain >= 1 labels, also row sums of A143395, A143396 and A143397.
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4
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1, 1, 4, 17, 89, 552, 3895, 30641, 265186, 2497551, 25373097, 276105106, 3199697517, 39297401197, 509370849148, 6943232742493, 99217486649933, 1482237515573624, 23093484367004715, 374416757914118941, 6304680593346141746
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..100
Index entries for sequences related to rooted trees
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FORMULA
| a(n) = Sum_{k=0..n} Sum_{t=k..n} C(n,t) * stirling2(t,k)*k^(n-t).
a(n) = Sum_{k=0..n} Sum_{t=0..k} C(n,k) * stirling2(k,t)*t^(n-k).
a(n) = Sum_{k=0..n} Sum_{t=0..k} C(n,k-t) * stirling2(n-(k-t),t)*t^(k-t).
E.g.f.: exp(exp(x)*(exp(x)-1)). [From Vladeta Jovovic, Dec 08 2008]
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EXAMPLE
| a(2) = 4, because there are 4 forests for 2 labels: {1,2}, {1}{2}, {1}<-2, {2}<-1.
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MAPLE
| with(combinat): a:= n-> add (add (binomial(n, t)* stirling2(t, k)* k^(n-t), t=k..n), k=0..n): seq (a(n), n=0..26);
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CROSSREFS
| Cf. A143395, A143396, A143397, A048993, A008277, A007318.
Sequence in context: A114190 A135168 A058279 * A141154 A112354 A020011
Adjacent sequences: A143402 A143403 A143404 * A143406 A143407 A143408
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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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