A230345 Number of permutations of [2n+5] in which the longest increasing run has length n+5.

1, 12, 181, 3322, 72540, 1845480, 53749920, 1766525760, 64739122560, 2619453513600, 116043825744000, 5588681114016000, 290812286052288000, 16263827918642304000, 973009916329651200000, 62017234027123415040000, 4195886889891954216960000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+5 in the permutations of [2n+5].

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+11*n, 2*(2*n+5)*(n+2)*
      (n^3+12*n^2+42*n+41)*a(n-1)/((n+7)*(n^3+9*n^2+21*n+10)))
    end:
seq(a(n), n=0..25);

Formula

a(n) = (n^3+12*n^2+42*n+41)*(2*n+5)!/(n+7)! for n>0, a(0) = 1.

a(n) = A008304(2*n+5,n+5) = A122843(2*n+5,n+5).