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A230251
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Number of permutations of [2n+1] in which the longest increasing run has length n+1.
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3
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1, 4, 41, 602, 11304, 257400, 6881160, 211170960, 7315701120, 282398538240, 12019910112000, 559278036979200, 28242651241728000, 1538394175334016000, 89912239244860032000, 5612575361948755200000, 372687441873534627840000, 26231028469670851706880000
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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+1 in the permutations of [2n+1].
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LINKS
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FORMULA
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For n>0, a(n) = (5+6*n+4*n^2+n^3)*(2*n+1)!/(n+3)!. - Vaclav Kotesovec, Oct 15 2013
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 1+3*n,
2*n*(2*n+1)*(n^3+4*n^2+6*n+5)*a(n-1)/((n+3)*(n^3+n^2+n+2)))
end:
seq(a(n), n=0..25);
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MATHEMATICA
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Flatten[{1, Table[(5+6*n+4*n^2+n^3)*(2*n+1)!/(n+3)!, {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 15 2013 *)
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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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