A128634 - OEIS

%I #28 Sep 08 2022 08:45:30

%S 0,2,8,26,82,262,856,2858,9722,33590,117570,416022,1485798,5348878,

%T 19389688,70715338,259289578,955277398,3534526378,13128240838,

%U 48932534038,182965127278,686119227298,2579808294646,9723892802902,36734706144302,139067101832006,527495903500718

%N Number of parallel permutations of length n.

%H G. C. Greubel, <a href="/A128634/b128634.txt">Table of n, a(n) for n = 1..1000</a>

%H T. Mansour and S. Severini, <a href="http://arxiv.org/abs/math/0603225">Grid polygons from permutations and their enumeration by the kernel method</a>, arXiv:math/0603225 [math.CO], 2006.

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

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

%F a(n) = 2*A001453(n) for n > 1. - _J. M. Bergot_, Sep 03 2013

%F a(n)= Sum_{r=0..n} A214292(n, r)^2. - _J. M. Bergot_, Sep 04 2013

%p c:=binomial(2*n,n)/(n+1); seq(2*(c(n)-1), n=1..30); # _G. C. Greubel_, Dec 02 2019

%t Table[2 (CatalanNumber[n] - 1), {n, 30}] (* _Vincenzo Librandi_, Jul 22 2015 *)

%o (PARI) vector(30, n, 2*(binomial(2*n,n)/(n+1) -1) ) \\ _Michel Marcus_, Jul 21 2015

%o (Magma) [2*(Catalan(n)-1): n in [1..40]]; // _Vincenzo Librandi_, Jul 22 2015

%o (Sage) [2*(catalan_number(n) -1) for n in (1..30)] # _G. C. Greubel_, Dec 02 2019

%o (GAP) List([1..30], n-> 2*(Binomial(2*n, n)/(n+1) -1) ); # _G. C. Greubel_, Dec 02 2019

%Y Cf. A001453, A068875, A214292.

%K nonn

%O 1,2

%A _Ralf Stephan_, May 08 2007

%E More terms from _Michel Marcus_, Jul 21 2015

%E Offset changed by _G. C. Greubel_, Dec 02 2019