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A262035
Number of permutations of [2n+1] beginning with exactly n ascents.
3
1, 2, 15, 168, 2520, 47520, 1081080, 28828800, 882161280, 30474662400, 1173274502400, 49819040409600, 2313026876160000, 116576554558464000, 6338850154116480000, 369890550169620480000, 23056510960573009920000, 1529010726859052236800000
OFFSET
0,2
LINKS
FORMULA
E.g.f.: (1-2*x)/(4*sqrt(1-4*x)*x^2)+(2*x^2-1)/(4*x^2).
a(n) = 2*(n+1)*(2*n+1)*a(n-1)/(n+2) for n>1, a(n) = n+1 for n<=1.
a(n) = (2*n+1)!/(n+1)! - floor((2*n+2)!/((n+1)!*(n+1)*(n+2)*2)).
a(n) = A262033(2n+1) - A262034(2n+1).
EXAMPLE
a(0) = 1: 1.
a(1) = 2: 132, 231.
a(2) = 15: 12435, 12534, 12543, 13425, 13524, 13542, 14523, 14532, 23415, 23514, 23541, 24513, 24531, 34512, 34521.
MAPLE
a:= proc(n) option remember; `if`(n<2, n+1,
2*(n+1)*(2*n+1)*a(n-1)/(n+2))
end:
seq(a(n), n=0..20);
CROSSREFS
Sequence in context: A153852 A177396 A324151 * A264793 A228840 A117667
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 08 2015
STATUS
approved