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A230342 Number of permutations of [2n+2] in which the longest increasing run has length n+2. 3
1, 6, 67, 1024, 19710, 456720, 12372360, 383685120, 13406178240, 521194867200, 22318001798400, 1043827513344000, 52949040240096000, 2895555891900672000, 169823181579891840000, 10633812541718446080000, 708077586604965857280000, 49962245750984840232960000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

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

FORMULA

a(n) = (n^3+6*n^2+12*n+11)*(2*n+2)!/(n+4)! for n>0, a(0) = 1.

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

MAPLE

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

      (n^3+6*n^2+12*n+11)*a(n-1)/((n+4)*(n^3+3*n^2+3*n+4)))

    end:

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

CROSSREFS

A diagonal of A008304, A122843.

Sequence in context: A024203 A231598 A073562 * A239301 A121958 A177555

Adjacent sequences:  A230339 A230340 A230341 * A230343 A230344 A230345

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 16 2013

STATUS

approved

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Last modified April 25 08:30 EDT 2017. Contains 285348 sequences.