A230348 Number of permutations of [2n+8] in which the longest increasing run has length n+8.

1, 18, 349, 7672, 192240, 5454144, 173606040, 6143195520, 239656253760, 10231052832000, 474832908950400, 23819880180096000, 1284985968634368000, 74207855717259264000, 4569213387521502720000, 298885288012537901875200, 20702796608070625112064000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+8 in the permutations of [2n+8].

Links

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

Crossrefs

A diagonal of A008304, A122843.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 1+17*n, 2*(n+4)*(2*n+7)*
      (n^3+18*n^2+90*n+89)*a(n-1)/((n+10)*(n^3+15*n^2+57*n+16)))
    end:
seq(a(n), n=0..25);

Formula

a(n) = (n^3+18*n^2+90*n+89)*(2*n+8)!/(n+10)! for n>0, a(0) = 1.

a(n) = A008304(2*n+8,n+8) = A122843(2*n+8,n+8).