A230349 Number of permutations of [2n+9] in which the longest increasing run has length n+9.

1, 20, 417, 9690, 253776, 7465176, 244906200, 8891411760, 354610872000, 15432114297600, 728406536457600, 37090538241120000, 2027740775284224000, 118512161081233920000, 7376476698319125196800, 487273386402209523916800, 34055074238462266429440000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+9 in the permutations of [2n+9].

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+19*n, 2*(2*n+9)*(n+4)*
      (n^3+20*n^2+110*n+109)*a(n-1)/((n+11)*(n^3+17*n^2+73*n+18)))
    end:
seq(a(n), n=0..25);

Formula

a(n) = (n^3+20*n^2+110*n+109)*(2*n+9)!/(n+11)! for n>0, a(0) = 1.

a(n) = A008304(2*n+9,n+9) = A122843(2*n+9,n+9).