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A317281 Number of permutations of [n] with exactly one increasing run of even length. 2
1, 4, 12, 52, 299, 1750, 11195, 83074, 675304, 5880354, 55691345, 570430818, 6235219145, 72578854088, 898625380692, 11776375141808, 162751388533495, 2367374376626798, 36156236738459671, 578320016708416430, 9668632218886209536, 168657264917156460894 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 7 09:43 EST 2023. Contains 360115 sequences. (Running on oeis4.)