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A230350
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Number of permutations of [2n+10] in which the longest increasing run has length n+10.
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3
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1, 22, 491, 12032, 328950, 10027440, 339006360, 12628788480, 515033719200, 22855760928000, 1097589192336000, 56754471481344000, 3145763658989952000, 186150029203211673600, 11717355323144959488000, 781981263963810054144000, 55165533654753963657216000
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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+10 in the permutations of [2n+10].
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..300
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FORMULA
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a(n) = (n^3+22*n^2+132*n+131)*(2*n+10)!/(n+12)! for n>0, a(0) = 1.
a(n) = A008304(2*n+10,n+10) = A122843(2*n+10,n+10).
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MAPLE
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a:= proc(n) option remember; `if`(n<2, 1+21*n, 2*(n+5)*(2*n+9)*
(n^3+22*n^2+132*n+131)*a(n-1)/((n+12)*(n^3+19*n^2+91*n+20)))
end:
seq(a(n), n=0..25);
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CROSSREFS
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A diagonal of A008304, A122843.
Sequence in context: A285876 A041221 A041926 * A180780 A121904 A158629
Adjacent sequences: A230347 A230348 A230349 * A230351 A230352 A230353
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 16 2013
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STATUS
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approved
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