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A230349 Number of permutations of [2n+9] in which the longest increasing run has length n+9. 3
1, 20, 417, 9690, 253776, 7465176, 244906200, 8891411760, 354610872000, 15432114297600, 728406536457600, 37090538241120000, 2027740775284224000, 118512161081233920000, 7376476698319125196800, 487273386402209523916800, 34055074238462266429440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+9 in the permutations of [2n+9].

LINKS

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

FORMULA

a(n) = (n^3+20*n^2+110*n+109)*(2*n+9)!/(n+11)! for n>0, a(0) = 1.

a(n) = A008304(2*n+9,n+9) = A122843(2*n+9,n+9).

MAPLE

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);

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A196740 A196898 A068772 * A158601 A268738 A215290

Adjacent sequences:  A230346 A230347 A230348 * A230350 A230351 A230352

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 16 2013

STATUS

approved

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Last modified May 23 18:24 EDT 2017. Contains 286926 sequences.