A214624 Braid numbers B((2)^n->(2)^n).

1, 1, 16, 504, 28800, 2620800, 348364800, 63707212800, 15343379251200, 4707627724800000, 1792664637603840000, 829619584788234240000, 458592296933263933440000, 298435681233688170332160000, 225843218230899155927040000000, 196652982274555440023470080000000

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..15.

J. de Ruiter, Counting Classes of Klondike Solitaire Configurations, Master's Thesis (2012), 48-58.

Formula

a(n) = (2n)!-n^2(2n-2)!.

a(n) = (2n)!*(3n-2)/(4n-2).

a(n) = a(n-1)*2n(2n-3)(3n-2)/(3n-5).

a(n) = Sum(a(n-i)*C(n,i)C(n-1,i-1)i!(i-1)!(2^(2i-1)-1), i=1..n).

a(n) = Sum(a(i)*n!(n-1)(2^(2n-2i-1)-1)/(i!)^2, i=0..n-1).

a(n) = Sum(a(i)*(n!!(n-1)!!/(i!!)^2-n!(n-1)!/(i!)^2, i=0..n-1).

Prog

(PARI) a(n) = (2*n)!*(3*n-2)/(4*n-2); \\ Michel Marcus, Aug 18 2013

Crossrefs

Sequence in context: A209214 A183890 A250400 * A322888 A291852 A301845

Adjacent sequences: A214621 A214622 A214623 * A214625 A214626 A214627

Keyword

nonn

Author

Johan de Ruiter, Jul 23 2012

Extensions

More terms from Michel Marcus, Aug 18 2013

Status

approved