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A156769
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a(n) = denominator(2^(2*n-2)/factorial(2*n-1)).
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13
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1, 3, 15, 315, 2835, 155925, 6081075, 638512875, 10854718875, 1856156927625, 194896477400625, 49308808782358125, 3698160658676859375, 1298054391195577640625, 263505041412702261046875
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OFFSET
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1,2
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COMMENTS
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Resembles A036279, the denominators in the Taylor series for tan(x). The first difference occurs at a(12).
The numerators of the two formulas for this sequence lead to A001316, Gould's sequence.
Stephen Crowley indicated on Aug 25 2008 that a(n) = denominator(Zeta(2*n)/Zeta(1-2*n)) and here numerator((Zeta(2*n)/Zeta(1-2*n))/(2*(-1)^(n)*(Pi)^(2*n))) leads to Gould's sequence.
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LINKS
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FORMULA
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a(n) = denominator( Product_{k=1..n-1} (2/(k*(2*k+1)) ).
G.f.: (1/2)*z^(1/2)*sinh(2*z^(1/2)).
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MAPLE
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a := n ->(2*n-1)!*2^(add(i, i=convert(n-1, base, 2))-2*n+2); # Peter Luschny, May 02 2009
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MATHEMATICA
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a[n_] := Denominator[4^(n-1)/(2n-1)!];
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PROG
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(Magma) [Denominator(4^(n-1)/Factorial(2*n-1)): n in [1..25]]; // G. C. Greubel, Jun 19 2021
(Sage) [denominator(4^(n-1)/factorial(2*n-1)) for n in (1..25)] # G. C. Greubel, Jun 19 2021
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CROSSREFS
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Cf. A036279 Denominators in Taylor series for tan(x).
Cf. A001316 Gould's sequence appears in the numerators.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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