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A321234
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Denominator of series expansion of the hypergeometric series 3F2([1/2, 1, 1], [3/2, 3/2], x).
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0
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1, 9, 75, 245, 2835, 7623, 39039, 96525, 1859715, 4387955, 20369349, 46646691, 422524375, 947754675, 4217257575, 9316746045, 327288272355, 714666904875, 3105965056425, 6720018279975, 57930003736605, 124404851229945, 532600050191625, 1136728029829275, 19356624110780775
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = numerator(binomial(2*n, n)/4^n) * (2*n+1)^2. - G. C. Greubel, Dec 07 2018
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MAPLE
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a:=n->(2*n+1)^2*binomial(2*n, n)/4^n: seq(numer(a(n)), n=0..25); # Muniru A Asiru, Dec 08 2018
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MATHEMATICA
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Denominator[CoefficientList[Series[HypergeometricPFQ[{1/2, 1, 1}, {3/2, 3/2}, c], {c, 0, 20}], c]]
Table[(2*n+1)^2*Numerator[Binomial[2*n, n]/4^n], {n, 0, 30}] (* G. C. Greubel, Dec 07 2018 *)
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PROG
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(PARI) vector(30, n, n--; numerator(binomial(2*n, n)/4^n)*(2*n+1)^2) \\ G. C. Greubel, Dec 07 2018
(Magma) [Numerator(Binomial(2*n, n)/4^n)*(2*n+1)^2: n in [0..30]]; // G. C. Greubel, Dec 07 2018
(Sage) [numerator(binomial(2*n, n)/4^n)*(2*n+1)^2 for n in range(30)] # G. C. Greubel, Dec 07 2018
(GAP) List([0..30], n -> NumeratorRat(Binomial(2*n, n)/4^n)*(2*n+1)^2); # G. C. Greubel, Dec 07 2018
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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