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Search: id:A144259
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| A144259 |
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Number of forests of trees on n or fewer nodes using a subset of labels 1..n, also row sums of triangle A144258. |
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+0
2
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| 1, 2, 5, 17, 83, 577, 5425, 65221, 959145, 16703045, 336294539, 7687013743, 196668883339, 5568107204467, 172833125462925, 5836126964882633, 212987232417299345, 8353651173273885025, 350415859403143234243
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Index entries for sequences related to trees
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FORMULA
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a(n) = Sum_{k=0..n} A144258(n,k).
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EXAMPLE
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a(2) = 5, because there are 5 forests of trees on 2 or less nodes using a subset of labels 1,2:
..... ..... ..... ..... .....
..... .1... ...2. .1.2. .1-2.
..... ..... ..... ..... .....
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MAPLE
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T:= proc(n, k) option remember; if k=0 then 2^n elif k<0 or n<=k then 0 elif k=n-1 then n^(n-2) else add (binomial (n-1, j) *T(j+1, j) *T(n-1-j, k-j), j=0..k) fi end: a:= n-> add (T(n, k), k=0..n): seq (a(n), n=0..20);
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CROSSREFS
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Cf. A144258, A007318, A000142.
Sequence in context: A098540 A079574 A032262 this_sequence A079805 A162038 A162039
Adjacent sequences: A144256 A144257 A144258 this_sequence A144260 A144261 A144262
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 16 2008
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