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A282296
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a(n) is the denominator of Sum_{k=0..n} Catalan(k)/(2^(2k)(n-k+1)^2).
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2
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1, 2, 144, 576, 57600, 4800, 7526400, 36126720, 6502809600, 6502809600, 899245670400, 3596982681600, 3404184409866240, 2836820341555200, 45389125464883200, 726226007438131200, 228959253981403545600, 20767279272689664, 1499397563488193740800, 67818905179312147660800, 2984031827889734497075200
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OFFSET
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0,2
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COMMENTS
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The series A282294(n)/a(n) is absolutely convergent to Pi^2/3.
It seems that each a(n)>1 is a product of primes p<=n+2.
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LINKS
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MATHEMATICA
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a[n_]=Sum[CatalanNumber[k]/(2^(2k)(n-k+1)^2), {k, 0, n}]; Denominator /@a/@ Range[0, 20]
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PROG
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(PARI) C(n) = binomial(2*n, n)/(n+1);
a(n) = denominator(sum(k=0, n, C(k)/(2^(2*k)*(n-k+1)^2))); \\ Michel Marcus, Feb 12 2017
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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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