A230343 Number of permutations of [2n+3] in which the longest increasing run has length n+3.

1, 8, 99, 1602, 32010, 761904, 21064680, 663848640, 23500653120, 923616691200, 39914540709120, 1881558401184000, 96096062174112000, 5286518167746816000, 311689569962010240000, 19608741674518284288000, 1311187373310480906240000, 92868537238628772741120000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+3 in the permutations of [2n+3].

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+7*n, 2*(2*n+3)*(n+1)*
      (n^3+8*n^2+20*n+19)*a(n-1)/((n+5)*(n^3+5*n^2+7*n+6)))
    end:
seq(a(n), n=0..25);

Formula

a(n) = (n^3+8*n^2+20*n+19)*(2*n+3)!/(n+5)! for n>0, a(0) = 1.

a(n) = A008304(2*n+3,n+3) = A122843(2*n+3,n+3).