A230382 Number of ascending runs of length n in the permutations of [2n].

1, 2, 21, 312, 5880, 133920, 3575880, 109549440, 3788104320, 145957593600, 6201593798400, 288084016281600, 14525808782284800, 790129980896256000, 46120599397192320000, 2875600728738017280000, 190740227037467627520000, 13411608375592258191360000

Offset: 0

Author

Alois P. Heinz, Oct 17 2013

Keywords

• nonn

Links

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

Crossrefs

A diagonal of A122843.

Programs

Maple

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

Formula

For n>0, a(n) = (n^2+n+1)*(2*n)!/((n+2)*n!). - Vaclav Kotesovec, Oct 18 2013