This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128634 #28 Sep 08 2022 08:45:30 %S A128634 0,2,8,26,82,262,856,2858,9722,33590,117570,416022,1485798,5348878, %T A128634 19389688,70715338,259289578,955277398,3534526378,13128240838, %U A128634 48932534038,182965127278,686119227298,2579808294646,9723892802902,36734706144302,139067101832006,527495903500718 %N A128634 Number of parallel permutations of length n. %H A128634 G. C. Greubel, <a href="/A128634/b128634.txt">Table of n, a(n) for n = 1..1000</a> %H A128634 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 A128634 a(n) = -2 + 2 * binomial(2*n,n)/(n+1). %F A128634 a(n) = -2 + A068875(n+1). %F A128634 a(n) = 2*A001453(n) for n > 1. - _J. M. Bergot_, Sep 03 2013 %F A128634 a(n)= Sum_{r=0..n} A214292(n, r)^2. - _J. M. Bergot_, Sep 04 2013 %p A128634 c:=binomial(2*n,n)/(n+1); seq(2*(c(n)-1), n=1..30); # _G. C. Greubel_, Dec 02 2019 %t A128634 Table[2 (CatalanNumber[n] - 1), {n, 30}] (* _Vincenzo Librandi_, Jul 22 2015 *) %o A128634 (PARI) vector(30, n, 2*(binomial(2*n,n)/(n+1) -1) ) \\ _Michel Marcus_, Jul 21 2015 %o A128634 (Magma) [2*(Catalan(n)-1): n in [1..40]]; // _Vincenzo Librandi_, Jul 22 2015 %o A128634 (Sage) [2*(catalan_number(n) -1) for n in (1..30)] # _G. C. Greubel_, Dec 02 2019 %o A128634 (GAP) List([1..30], n-> 2*(Binomial(2*n, n)/(n+1) -1) ); # _G. C. Greubel_, Dec 02 2019 %Y A128634 Cf. A001453, A068875, A214292. %K A128634 nonn %O A128634 1,2 %A A128634 _Ralf Stephan_, May 08 2007 %E A128634 More terms from _Michel Marcus_, Jul 21 2015 %E A128634 Offset changed by _G. C. Greubel_, Dec 02 2019