OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)
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
KEYWORD
nonn,nice
AUTHOR
Vaclav Kotesovec, Apr 27 2011
STATUS
approved