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 A317281 Number of permutations of [n] with exactly one increasing run of even length. 2

%I

%S 1,4,12,52,299,1750,11195,83074,675304,5880354,55691345,570430818,

%T 6235219145,72578854088,898625380692,11776375141808,162751388533495,

%U 2367374376626798,36156236738459671,578320016708416430,9668632218886209536,168657264917156460894

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

%H Alois P. Heinz, <a href="/A317281/b317281.txt">Table of n, a(n) for n = 2..473</a>

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

%p b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,

%p add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+

%p add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 2)

%p end:

%p a:= n-> coeff(b(n, 0\$2), x, 1):

%p seq(a(n), n=2..25);

%Y Column k=1 of A097592.

%K nonn

%O 2,2

%A _Alois P. Heinz_, Jul 25 2018

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Last modified March 24 04:28 EDT 2023. Contains 361454 sequences. (Running on oeis4.)