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A230345 Number of permutations of [2n+5] in which the longest increasing run has length n+5. 3
1, 12, 181, 3322, 72540, 1845480, 53749920, 1766525760, 64739122560, 2619453513600, 116043825744000, 5588681114016000, 290812286052288000, 16263827918642304000, 973009916329651200000, 62017234027123415040000, 4195886889891954216960000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+5 in the permutations of [2n+5].

LINKS

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

FORMULA

a(n) = (n^3+12*n^2+42*n+41)*(2*n+5)!/(n+7)! for n>0, a(0) = 1.

a(n) = A008304(2*n+5,n+5) = A122843(2*n+5,n+5).

MAPLE

a:= proc(n) option remember; `if`(n<2, 1+11*n, 2*(2*n+5)*(n+2)*

      (n^3+12*n^2+42*n+41)*a(n-1)/((n+7)*(n^3+9*n^2+21*n+10)))

    end:

seq(a(n), n=0..25);

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A001814 A013924 A145560 * A166773 A202632 A218886

Adjacent sequences:  A230342 A230343 A230344 * A230346 A230347 A230348

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 16 2013

STATUS

approved

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Last modified March 24 00:18 EDT 2017. Contains 283983 sequences.