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A230345
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Number of permutations of [2n+5] in which the longest increasing run has length n+5.
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3
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1, 12, 181, 3322, 72540, 1845480, 53749920, 1766525760, 64739122560, 2619453513600, 116043825744000, 5588681114016000, 290812286052288000, 16263827918642304000, 973009916329651200000, 62017234027123415040000, 4195886889891954216960000
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OFFSET
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0,2
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COMMENTS
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Also the number of ascending runs of length n+5 in the permutations of [2n+5].
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LINKS
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FORMULA
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a(n) = (n^3+12*n^2+42*n+41)*(2*n+5)!/(n+7)! for n>0, a(0) = 1.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 1+11*n, 2*(2*n+5)*(n+2)*
(n^3+12*n^2+42*n+41)*a(n-1)/((n+7)*(n^3+9*n^2+21*n+10)))
end:
seq(a(n), n=0..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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