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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
OFFSET
2,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 25 2018
STATUS
approved