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%I #16 Aug 18 2013 19:07:37
%S 1,1,16,504,28800,2620800,348364800,63707212800,15343379251200,
%T 4707627724800000,1792664637603840000,829619584788234240000,
%U 458592296933263933440000,298435681233688170332160000,225843218230899155927040000000,196652982274555440023470080000000
%N Braid numbers B((2)^n->(2)^n).
%C The number of different possible outcomes when starting with n piles of 2 distinct playing cards and repeatedly moving a top card from either of these n piles to one of n new piles, until all new piles have height 2.
%H J. de Ruiter, <a href="http://www.liacs.nl/assets/Masterscripties/2012-09JohandeRuiter.pdf">Counting Classes of Klondike Solitaire Configurations</a>, Master's Thesis (2012), 48-58.
%F a(n) = (2n)!-n^2(2n-2)!.
%F a(n) = (2n)!*(3n-2)/(4n-2).
%F a(n) = a(n-1)*2n(2n-3)(3n-2)/(3n-5).
%F a(n) = Sum(a(n-i)*C(n,i)C(n-1,i-1)i!(i-1)!(2^(2i-1)-1), i=1..n).
%F a(n) = Sum(a(i)*n!(n-1)(2^(2n-2i-1)-1)/(i!)^2, i=0..n-1).
%F a(n) = Sum(a(i)*(n!!(n-1)!!/(i!!)^2-n!(n-1)!/(i!)^2, i=0..n-1).
%o (PARI) a(n) = (2*n)!*(3*n-2)/(4*n-2); \\ _Michel Marcus_, Aug 18 2013
%K nonn
%O 0,3
%A _Johan de Ruiter_, Jul 23 2012
%E More terms from _Michel Marcus_, Aug 18 2013
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