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

2,2

Links

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

Formula

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

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);

Crossrefs

Column k=1 of A097592.

Sequence in context: A129841 A277431 A065525 * A190342 A262745 A180381

Adjacent sequences: A317278 A317279 A317280 * A317282 A317283 A317284

Keyword

nonn

Author

Alois P. Heinz, Jul 25 2018

Status

approved