A230347 Number of permutations of [2n+7] in which the longest increasing run has length n+7.

1, 16, 287, 5954, 142590, 3900480, 120466080, 4156079760, 158664456720, 6647965632000, 303540020784000, 15009431909472000, 799414492260384000, 45641465547245568000, 2781538377619921920000, 180263592116387619840000, 12381113998069012804608000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

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

Crossrefs

A diagonal of A008304, A122843.

Programs

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);

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).