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Search: id:A143404
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| A143404 |
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Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=9. |
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+0
2
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 135, 10065, 547965, 24336312, 934863930, 32189799070, 1017281878470, 30001945084683, 835898091070185, 22206607023852615, 566594907018764715, 13964270139973201114, 333991935681805199700
(list; graph; listen)
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OFFSET
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0,11
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COMMENT
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a(n) is also the number of forests of 9 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^9/ ((1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)(1-15x)(1-16x)(1-17x)(1-18*x)).
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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(9); seq (a(n), n=0..27);
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CROSSREFS
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9th column of A143395.
Adjacent sequences: A143401 A143402 A143403 this_sequence A143405 A143406 A143407
Sequence in context: A157734 A061073 A004005 this_sequence A051028 A076011 A132054
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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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