A230251 Number of permutations of [2n+1] in which the longest increasing run has length n+1.

1, 4, 41, 602, 11304, 257400, 6881160, 211170960, 7315701120, 282398538240, 12019910112000, 559278036979200, 28242651241728000, 1538394175334016000, 89912239244860032000, 5612575361948755200000, 372687441873534627840000, 26231028469670851706880000

Offset: 0

Author

Alois P. Heinz, Oct 13 2013

Keywords

• nonn

Comments

Also the number of ascending runs of length n+1 in the permutations of [2n+1].

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Diagonal of A008304, A122843.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 1+3*n,
      2*n*(2*n+1)*(n^3+4*n^2+6*n+5)*a(n-1)/((n+3)*(n^3+n^2+n+2)))
    end:
seq(a(n), n=0..25);

Mathematica

Flatten[{1,Table[(5+6*n+4*n^2+n^3)*(2*n+1)!/(n+3)!,{n,1,20}]}] (* Vaclav Kotesovec, Oct 15 2013 *)

Formula

a(n) = A008304(2*n+1,n+1) = A122843(2*n+1,n+1).

For n>0, a(n) = (5+6*n+4*n^2+n^3)*(2*n+1)!/(n+3)!. - Vaclav Kotesovec, Oct 15 2013