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A230347
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Number of permutations of [2n+7] in which the longest increasing run has length n+7.
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3
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1, 16, 287, 5954, 142590, 3900480, 120466080, 4156079760, 158664456720, 6647965632000, 303540020784000, 15009431909472000, 799414492260384000, 45641465547245568000, 2781538377619921920000, 180263592116387619840000, 12381113998069012804608000
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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+7 in the permutations of [2n+7].
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LINKS
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FORMULA
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a(n) = (n^3+16*n^2+72*n+71)*(2*n+7)!/(n+9)! for n>0, a(0) = 1.
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 1+15*n, 2*(n+3)*(2*n+7)*
(n^3+16*n^2+72*n+71)*a(n-1)/((n+9)*(n^3+13*n^2+43*n+14)))
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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