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A143401
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Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=6.
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2
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0, 0, 0, 0, 0, 0, 1, 63, 2282, 62370, 1428987, 28979181, 537306484, 9302333040, 152587968533, 2396472657579, 36320866824606, 534421447961310, 7670116319449039, 107781064078390857, 1487396442778796648, 20208696810429799980, 270879169288278532905
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| a(n) is also the number of forests of 6 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..300
Index entries for sequences related to rooted trees
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FORMULA
| G.f.: x^6/((1-6x)(1-7x)(1-8x)(1-9x)(1-10x)(1-11x)(1-12x)).
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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(6); seq (a(n), n=0..27);
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CROSSREFS
| 6th column of A143395.
Sequence in context: A017726 A170932 A173191 * A075516 A004376 A094938
Adjacent sequences: A143398 A143399 A143400 * A143402 A143403 A143404
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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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