A230342 Number of permutations of [2n+2] in which the longest increasing run has length n+2.

1, 6, 67, 1024, 19710, 456720, 12372360, 383685120, 13406178240, 521194867200, 22318001798400, 1043827513344000, 52949040240096000, 2895555891900672000, 169823181579891840000, 10633812541718446080000, 708077586604965857280000, 49962245750984840232960000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

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

Crossrefs

A diagonal of A008304, A122843.

Programs

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);

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).