The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208529 Number of permutations of n > 1 having exactly 2 points on the boundary of their bounding square. 10
 2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, 174356582400, 2615348736000, 41845579776000, 711374856192000, 12804747411456000, 243290200817664000, 4865804016353280000, 102181884343418880000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS A bounding square for a permutation of n is the square with sides parallel to the coordinate axis containing (1,1) and (n,n), and the set of points P of a permutation p is the set {(k,p(k)) for 0 < k < n+1}. Sequences A098558 and A052849 have the same terms except for the first. - Joerg Arndt, Mar 03 2012 a(n) is the number of permutations of n symbols that commute with a transposition: a permutation p of {1,...,n} has exactly two points on the boundary of their bounding square if and only if p commutes with transposition (1, n). - Luis Manuel Rivera Martínez, Feb 27 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..200 E. Deutsch, Permutations and their bounding squares, Math Magazine, 85(1) (2012), 63. Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015. FORMULA a(n) = 2(n-2)!. G.f.: G(0), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 26 2013 G.f.: 2 + 2*x/Q(0), where Q(k) = 1 - 2*x*(2*k+1) - x^2*(2*k+1)*(2*k+2)/( 1 - 2*x*(2*k+2) - x^2*(2*k+2)*(2*k+3)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Sep 23 2013 a(n) = 2*n!/(n*(n-1)). - Vincenzo Librandi, Apr 15 2014 E.g.f.: 2 - (1 - x)*(2 + log(1/(1 - x)^2)). - Ilya Gutkovskiy, Mar 21 2018 EXAMPLE a(2) = 2 because {(1,1),(2,2)} and {(1,2),(2,1)} each have two points on the bounding square. MAPLE A208529:=n->2*(n-2)!; seq(A208529(n), n=2..25); # Wesley Ivan Hurt, Feb 27 2014 MATHEMATICA Table[2(n-2)!, {n, 2, 10}] FoldList[Times, 2, Range@21] (* Arkadiusz Wesolowski, May 08 2012 *) Table[2 n!/n, {n, 1, 40}] (* Vincenzo Librandi, Apr 15 2014 *) PROG (Python) import math def a(n):     return 2*math.factorial(n-2) (MAGMA) [2*Factorial(n)/n: n in [1..40]]; // Vincenzo Librandi, Apr 15 2014 (PARI) vector(33, n, 2*n!/n) /* Anders Hellström, Jul 07 2015 */ CROSSREFS Cf. A098916, A208528. Sequence in context: A287604 A007181 A100238 * A212660 A098774 A009264 Adjacent sequences:  A208526 A208527 A208528 * A208530 A208531 A208532 KEYWORD nonn,easy AUTHOR David Nacin, Feb 27 2012 STATUS approved

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

Last modified June 23 11:29 EDT 2021. Contains 345397 sequences. (Running on oeis4.)