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A230347 Number of permutations of [2n+7] in which the longest increasing run has length n+7. 3
1, 16, 287, 5954, 142590, 3900480, 120466080, 4156079760, 158664456720, 6647965632000, 303540020784000, 15009431909472000, 799414492260384000, 45641465547245568000, 2781538377619921920000, 180263592116387619840000, 12381113998069012804608000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the number of ascending runs of length n+7 in the permutations of [2n+7].

LINKS

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

FORMULA

a(n) = (n^3+16*n^2+72*n+71)*(2*n+7)!/(n+9)! for n>0, a(0) = 1.

a(n) = A008304(2*n+7,n+7) = A122843(2*n+7,n+7).

MAPLE

a:= proc(n) option remember; `if`(n<2, 1+15*n, 2*(n+3)*(2*n+7)*

      (n^3+16*n^2+72*n+71)*a(n-1)/((n+9)*(n^3+13*n^2+43*n+14)))

    end:

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

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A240336 A281341 A218517 * A182608 A225194 A027776

Adjacent sequences:  A230344 A230345 A230346 * A230348 A230349 A230350

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.