login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..365

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

Cf. A262033, A262034.

Sequence in context: A153852 A177396 A324151 * A264793 A228840 A117667

Adjacent sequences:  A262032 A262033 A262034 * A262036 A262037 A262038

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 08 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)