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A143400
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Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=5.
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1
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0, 0, 0, 0, 0, 1, 45, 1190, 24150, 416451, 6427575, 91549480, 1227283200, 15695180501, 193333245105, 2310273772170, 26927270656650, 307413790470151, 3449088814306635, 38132767214613260, 416342920938136500
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OFFSET
| 0,7
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COMMENTS
| a(n) is also the number of forests of 5 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| G.f.: x^5/((1-5x)(1-6x)(1-7x)(1-8x)(1-9x)(1-10x)).
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MAPLE
| 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(5); seq (a(n), n=0..27);
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CROSSREFS
| 5th column of A143395.
Sequence in context: A177728 A140346 A049447 * A173000 A004350 A199518
Adjacent sequences: A143397 A143398 A143399 * A143401 A143402 A143403
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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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