A317281 Number of permutations of [n] with exactly one increasing run of even length.

1, 4, 12, 52, 299, 1750, 11195, 83074, 675304, 5880354, 55691345, 570430818, 6235219145, 72578854088, 898625380692, 11776375141808, 162751388533495, 2367374376626798, 36156236738459671, 578320016708416430, 9668632218886209536, 168657264917156460894

Offset: 2

Author

Alois P. Heinz, Jul 25 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..473

Crossrefs

Column k=1 of A097592.

Programs

Maple

b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
      add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
      add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 2)
    end:
a:= n-> coeff(b(n, 0$2), x, 1):
seq(a(n), n=2..25);

Formula

a(n) ~ c * d^n * n^(n + 3/2), where d = 0.26695170015188549567... and c = 1.1281954524592228... - Vaclav Kotesovec, Jul 01 2019