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Search: id:A114362
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| A114362 |
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Numerator of zeta(4n)/zeta(2n)^2 (with a(0)=2 instead of -2). |
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+0
2
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| 2, 2, 6, 691, 7234, 523833, 3545461365, 3392780147, 15418642082434, 26315271553053477373, 261082718496449122051, 2530297234481911294093, 39265823582984723803743892829, 61628132164268458257532691681
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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zeta(4n)/zeta(2n)^2 is a rational value expressible in term of Bernoulli's numbers (A027641).
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FORMULA
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prod( (p^{2n}-1)/(p^{2n}+1)=zeta(4n)/zeta(2n)^2 where the product is over all the primes
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PROGRAM
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(PARI) z(n)=bernfrac(2*n)*(-1)^(n - 1)*2^(2*n-1)/(2*n)!; a(n)=if(n<1, 2, numerator(z(2*n)/z(n)^2))
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CROSSREFS
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Cf. A027641, A114363.
Sequence in context: A032117 A137244 A093909 this_sequence A013671 A019807 A063706
Adjacent sequences: A114359 A114360 A114361 this_sequence A114363 A114364 A114365
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KEYWORD
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frac,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 09 2006; corrected Feb 22 2006
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