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Search: id:A143399
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| A143399 |
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Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=4. |
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+0
2
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| 0, 0, 0, 0, 1, 30, 545, 7770, 95781, 1071630, 11192665, 111095490, 1060634861, 9822843030, 88799732385, 787259974410, 6869327386741, 59158464019230, 503954741177705, 4254156112792530, 35637875826743421, 296621138907400230
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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a(n) is also the number of forests of 4 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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G.f.: x^4/((1-4x)(1-5x)(1-6x)(1-7x)(1-8x)). a(n) = 30a(n-1) -355a(n-2) +2070a(n-3) -5944a(n-4) +6720a(n-5).
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MAPLE
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a := proc(k::nonnegint) local M; M := Matrix(k+1, (i, j)-> if (i=j-1) then 1 elif j=1 then [seq(-1* coeff (product (1-t*x, t=k..2*k), x, u), u=1..k+1)][i] else 0 fi); p-> (M^p)[1, k+1] end(4); seq (a (n), n=0..27);
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CROSSREFS
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4th column of A143395.
Sequence in context: A004327 A139626 A037961 this_sequence A075510 A028200 A028181
Adjacent sequences: A143396 A143397 A143398 this_sequence A143400 A143401 A143402
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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), Aug 12 2008
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