A128634 Number of parallel permutations of length n.

0, 2, 8, 26, 82, 262, 856, 2858, 9722, 33590, 117570, 416022, 1485798, 5348878, 19389688, 70715338, 259289578, 955277398, 3534526378, 13128240838, 48932534038, 182965127278, 686119227298, 2579808294646, 9723892802902, 36734706144302, 139067101832006, 527495903500718

Offset: 1

Author

Ralf Stephan, May 08 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• T. Mansour and S. Severini, Grid polygons from permutations and their enumeration by the kernel method, arXiv:math/0603225 [math.CO], 2006.

Crossrefs

Cf. A001453, A068875, A214292.

Programs

GAP

List([1..30], n-> 2*(Binomial(2*n, n)/(n+1) -1) ); # G. C. Greubel, Dec 02 2019

Magma

[2*(Catalan(n)-1): n in [1..40]]; // Vincenzo Librandi, Jul 22 2015

Maple

c:=binomial(2*n,n)/(n+1); seq(2*(c(n)-1), n=1..30); # G. C. Greubel, Dec 02 2019

Mathematica

Table[2 (CatalanNumber[n] - 1), {n, 30}] (* Vincenzo Librandi, Jul 22 2015 *)

PARI

vector(30, n, 2*(binomial(2*n,n)/(n+1) -1) ) \\ Michel Marcus, Jul 21 2015

Sage

[2*(catalan_number(n) -1) for n in (1..30)] # G. C. Greubel, Dec 02 2019

Formula

a(n) = -2 + 2 * binomial(2*n,n)/(n+1).

a(n) = -2 + A068875(n+1).

a(n) = 2*A001453(n) for n > 1. - J. M. Bergot, Sep 03 2013

a(n)= Sum_{r=0..n} A214292(n, r)^2. - J. M. Bergot, Sep 04 2013

Extensions

More terms from Michel Marcus, Jul 21 2015

Offset changed by G. C. Greubel, Dec 02 2019