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A268085
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a(n) = Catalan(n)^2*n.
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1
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0, 1, 8, 75, 784, 8820, 104544, 1288287, 16359200, 212751396, 2821056160, 38013731756, 519227905728, 7174705330000, 100136810390400, 1409850293610375, 20002637245262400, 285732116760449700, 4106497099278420000, 59341164471850545900, 861753537765219528000
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OFFSET
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0,3
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COMMENTS
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The series whose terms are the quotients a(n)/A013709(n) is convergent to 1-3/Pi.(see formula).
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 1-3/Pi. Q.E.D.
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LINKS
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FORMULA
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EXAMPLE
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For n=3 the a(3)= 75.
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MATHEMATICA
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Table[CatalanNumber[n]^2 n, {n, 0, 20}]
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PROG
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(PARI) a(n) = n*(binomial(2*n, n)/(n+1))^2; \\ Altug Alkan, Jan 26 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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