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A267987
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a(n) = Catalan(n)^2*(4n + 4).
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1
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4, 8, 48, 400, 3920, 42336, 487872, 5889312, 73616400, 945561760, 12412647104, 165878102208, 2249987591488, 30906422960000, 429157758816000, 6015361252737600, 85011208292365200, 1210159553338375200, 17338543308064440000, 249857534618318088000
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OFFSET
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0,1
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COMMENTS
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Numerator of the modified (4n+4) Wallis-Lambert series with denominator A013709 convergent to 4/Pi. Proof: Both the Wallis-Lambert-series-1=4/Pi-1 and the elliptic Euler-series=1-2/Pi are absolutely convergent series. Thus any linear combination of the terms of these series will be also absolutely convergent to the value of the linear combination of these series - in this case: 4/Pi. Q.E.D.
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LINKS
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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