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A267844
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a(n) = Catalan(n)^2*(4n + 3).
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1
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3, 7, 44, 375, 3724, 40572, 470448, 5705271, 71571500, 921922716, 12130541488, 162422308412, 2206718599344, 30354522550000, 422005129502400, 5921371233163575, 83761043464536300, 1193351781764231100, 17110404580326750000, 246734315435589111900
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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+3) Wallis-Lambert-series-1 with denominator A013709 convergent to 1. 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 to 1. Q.E.D.
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LINKS
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FORMULA
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a(n) = Catalan(n)^2*(4n + 3).
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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,frac
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AUTHOR
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STATUS
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approved
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