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A230350 Number of permutations of [2n+10] in which the longest increasing run has length n+10. 3
1, 22, 491, 12032, 328950, 10027440, 339006360, 12628788480, 515033719200, 22855760928000, 1097589192336000, 56754471481344000, 3145763658989952000, 186150029203211673600, 11717355323144959488000, 781981263963810054144000, 55165533654753963657216000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+10 in the permutations of [2n+10].

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

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).

MAPLE

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);

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A009966 A041221 A041926 * A180780 A121904 A158629

Adjacent sequences:  A230347 A230348 A230349 * A230351 A230352 A230353

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 16 2013

STATUS

approved

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Last modified March 24 00:16 EDT 2017. Contains 283985 sequences.