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A189790
Number of ways to place n nonattacking bishops on an n X n toroidal board.
3
1, 4, 6, 64, 120, 2304, 5040, 147456, 362880, 14745600, 39916800, 2123366400, 6227020800, 416179814400, 1307674368000, 106542032486400, 355687428096000, 34519618525593600, 121645100408832000, 13807847410237440000
OFFSET
1,2
FORMULA
a(n) = 2^n*((n/2)!)^2 if n is even and a(n) = n! if n is odd.
a(n) = n*(2*n-3)*a(n-2)-(n-3)*n*(n-2)^2*a(n-4). [Vaclav Kotesovec, Sep 26 2012]
E.g.f.: 1/(1-x)+x*arcsin(x)/(1-x^2)^(3/2). [Vaclav Kotesovec, Sep 26 2012]
MATHEMATICA
Table[If[EvenQ[n], 2^n*((n/2)!)^2, n!], {n, 1, 20}]
Table[n!*SeriesCoefficient[1/(1-x)+x*ArcSin[x]/(1-x^2)^(3/2), {x, 0, n}], {n, 1, 25}] (* Vaclav Kotesovec, Sep 26 2012 *)
CROSSREFS
Sequence in context: A132929 A154668 A363861 * A053489 A012898 A013080
KEYWORD
nonn,nice
AUTHOR
Vaclav Kotesovec, Apr 27 2011
STATUS
approved