A230344 Number of permutations of [2n+4] in which the longest increasing run has length n+4.

1, 10, 137, 2360, 49236, 1209936, 34288800, 1102187520, 39656131200, 1579837754880, 69064610186880, 3288126441600000, 169388400557376000, 9389435419203840000, 557323393281887232000, 35272416767753797632000, 2371290445442664345600000

Offset: 0

Author

Alois P. Heinz, Oct 16 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+4 in the permutations of [2n+4].

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+9*n, 2*(2*n+3)*(n+2)*
      (n^3+10*n^2+30*n+29)*a(n-1)/((n+6)*(n^3+7*n^2+13*n+8)))
    end:
seq(a(n), n=0..25);

Formula

a(n) = (n^3+10*n^2+30*n+29)*(2*n+4)!/(n+6)! for n>0, a(0) = 1.

a(n) = A008304(2*n+4,n+4) = A122843(2*n+4,n+4).