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A230349
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Number of permutations of [2n+9] in which the longest increasing run has length n+9.
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3
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1, 20, 417, 9690, 253776, 7465176, 244906200, 8891411760, 354610872000, 15432114297600, 728406536457600, 37090538241120000, 2027740775284224000, 118512161081233920000, 7376476698319125196800, 487273386402209523916800, 34055074238462266429440000
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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+9 in the permutations of [2n+9].
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LINKS
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FORMULA
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a(n) = (n^3+20*n^2+110*n+109)*(2*n+9)!/(n+11)! for n>0, a(0) = 1.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 1+19*n, 2*(2*n+9)*(n+4)*
(n^3+20*n^2+110*n+109)*a(n-1)/((n+11)*(n^3+17*n^2+73*n+18)))
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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