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A230346 Number of permutations of [2n+6] in which the longest increasing run has length n+6. 3
1, 14, 231, 4512, 103194, 2721600, 81591840, 2746068480, 102661518960, 4224849995520, 189917647920000, 9263565222912000, 487461283781472000, 27533206366009344000, 1661865400404937728000, 106768864984887705600000, 7275718977990226283520000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+6 in the permutations of [2n+6].

LINKS

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

FORMULA

a(n) = (n+5)*(n^2+9*n+11)*(2*n+6)!/(n+8)! for n>0, a(0) = 1.

a(n) = A008304(2*n+6,n+6) = A122843(2*n+6,n+6).

MAPLE

a:= proc(n) option remember; `if`(n<2, 1+13*n, 2*(2*n+5)*(n+5)*

      (n+3)*(n^2+9*n+11)*a(n-1)/((n+4)*(n+8)*(n^2+7*n+3)))

    end:

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

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A273625 A120048 A079563 * A280559 A222377 A220502

Adjacent sequences:  A230343 A230344 A230345 * A230347 A230348 A230349

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 16 2013

STATUS

approved

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Last modified August 17 17:27 EDT 2017. Contains 290648 sequences.