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

1,2

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.

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

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 *)

Prog

(PARI) vector(30, n, 2*(binomial(2*n, n)/(n+1) -1) ) \\ Michel Marcus, Jul 21 2015
(Magma) [2*(Catalan(n)-1): n in [1..40]]; // Vincenzo Librandi, Jul 22 2015
(Sage) [2*(catalan_number(n) -1) for n in (1..30)] # G. C. Greubel, Dec 02 2019
(GAP) List([1..30], n-> 2*(Binomial(2*n, n)/(n+1) -1) ); # G. C. Greubel, Dec 02 2019

Crossrefs

Cf. A001453, A068875, A214292.

Sequence in context: A126966 A002930 A060410 * A230904 A289595 A343485

Adjacent sequences: A128631 A128632 A128633 * A128635 A128636 A128637

Keyword

nonn

Author

Ralf Stephan, May 08 2007

Extensions

More terms from Michel Marcus, Jul 21 2015

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

Status

approved