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Search: id:A143403
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| A143403 |
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Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=8. |
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+0
2
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| 0, 0, 0, 0, 0, 0, 0, 0, 1, 108, 6510, 289080, 10550067, 335170836, 9597839680, 253489991040, 6275077781973, 147318890173884, 3309320153700210, 71623038281001480, 1501654449863348119, 30633757929391948452
(list; graph; listen)
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OFFSET
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0,10
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COMMENT
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a(n) is also the number of forests of 8 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^8/((1-8x)(1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)(1-15x)(1-16x)).
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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(8); seq (a(n), n=0..27);
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CROSSREFS
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8th column of A143395.
Sequence in context: A035812 A054624 A147821 this_sequence A132053 A164748 A113853
Adjacent sequences: A143400 A143401 A143402 this_sequence A143404 A143405 A143406
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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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