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A153741
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Number of elements in wreath product C_2 wr S_n that alternate up/not-up with respect to a weak product ordering.
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1
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2, 3, 14, 49, 376, 1987, 21328, 150337, 2074624, 18279971, 308317184, 3259985969, 64981320704, 801591982115, 18436312819712, 259914703640065, 6774998673915904, 107452993132016323, 3130412454801965056
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OFFSET
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1,1
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LINKS
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FORMULA
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E.g.f.: (1 + sin(x) + x*cos(x))/(cos(x) - x*sin(x)).
a(n) ~ c * n! / r^(n+1), where r = 0.860333589... (=A069855) is the root of the equation sin(r)*r = cos(r), and c = 2/((2+r^2)*sin(r)) = 0.9628268573779... if n is even and c = 2-2/(r^2+2*r*tan(r)) = 1.2701193119933... if n is odd. - Vaclav Kotesovec, Sep 25 2013
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EXAMPLE
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Viewing elements in one-line notation as a list of ordered pairs with first entries in [2] and second entries forming a permutation in S_n, two of the 6 up/not-up elements for n=3 are (1,2) (2,3) (1,1) and (1,1) (1,3) (2,2). Note that the first element goes up/down and the second goes up/not-up with respect to the weak product ordering on ordered pairs.
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MATHEMATICA
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Rest[CoefficientList[Series[(1+Sin[x]+x*Cos[x])/(Cos[x]-x*Sin[x]), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Sep 25 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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