A230346 Number of permutations of [2n+6] in which the longest increasing run has length n+6.

1, 14, 231, 4512, 103194, 2721600, 81591840, 2746068480, 102661518960, 4224849995520, 189917647920000, 9263565222912000, 487461283781472000, 27533206366009344000, 1661865400404937728000, 106768864984887705600000, 7275718977990226283520000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

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

Crossrefs

A diagonal of A008304, A122843.

Programs

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);

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).