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A295231
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Numerators of (-1)^(n+1) * (2*n)! * (2^(2*n)+1)/(B_{2*n} * 2^(4*n-1)), where B_{n} is the Bernoulli number.
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2
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-4, 15, 765, 61425, 1214325, 95893875, 2615987248875, 298915241625, 10670785663663125, 10218227413637368125, 1605716856726047690625, 56404413605424162403125, 3387648475383059302662121875, 744538093174369303262578125
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OFFSET
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0,1
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COMMENTS
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Pi^(2*n) > a(n)/A295232(n) for n > 0.
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LINKS
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EXAMPLE
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Zeta(2) = Pi^2/6 > 1 + 1/2^2, so Pi^2 > 15/2.
Zeta(4) = Pi^4/90 > 1 + 1/2^4, so Pi^4 > 765/8.
Zeta(6) = Pi^6/945 > 1 + 1/2^6, so Pi^6 > 61425/64.
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PROG
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(PARI) {a(n) = numerator((-1)^(n+1)*(2*n)!*(2^(2*n)+1)/(bernfrac(2*n)*2^(4*n-1)))}
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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