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A156648
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Decimal expansion of Product_{k>=1} (1 + 1/k^2).
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16
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3, 6, 7, 6, 0, 7, 7, 9, 1, 0, 3, 7, 4, 9, 7, 7, 7, 2, 0, 6, 9, 5, 6, 9, 7, 4, 9, 2, 0, 2, 8, 2, 6, 0, 6, 6, 6, 5, 0, 7, 1, 5, 6, 3, 4, 6, 8, 2, 7, 6, 3, 0, 2, 7, 7, 4, 7, 8, 0, 0, 3, 5, 9, 3, 5, 5, 7, 4, 4, 7, 3, 2, 4, 1, 1, 1, 0, 2, 2, 0, 7, 3, 2, 1, 3, 2, 5, 5, 9, 2, 6, 5, 9, 0, 3, 2, 3, 0, 2, 3, 5, 2, 8, 7, 5
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OFFSET
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1,1
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COMMENTS
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Consider the value at s = 2 of the partition zeta functions zeta_{type}(s), where the defining sum runs over partitions into 'type' parts, where 'type' is 'even', 'prime' or 'distinct'. (For the precise definitions see R. Schneider's dissertation.) Then
zeta_{prime}(2) = Pi^2/6 = A013661;
zeta_{distinct}(2) = sinh(Pi)/Pi, this constant. - Peter Luschny, Aug 11 2021
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REFERENCES
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Reinhold Remmert, Classical topics in complex function theory, Vol. 172 of Graduate Texts in Mathematics, p. 12, Springer, 1997.
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LINKS
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FORMULA
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Equals sinh(Pi)/Pi.
Binomial(2, 1+i) = 1/(i!*(-i)!) (where x! means Gamma(x+1)). - Robert G. Wilson v, Feb 23 2015
Equals Product_{k>=1} (1+2/(k*(k+2))). - Amiram Eldar, Aug 16 2020
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EXAMPLE
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3.676077910374977720695697492028260666507156346827630277478003593557447324111... = (1+1)*(1+1/4)*(1+1/9)*(1+1/16)*(1+1/25)*...
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MAPLE
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evalf(sinh(Pi)/Pi) ;
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MATHEMATICA
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RealDigits[Sinh[Pi]/Pi, 10, 111][[1]] (* or *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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