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A080729
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Decimal expansion of the infinite product of zeta functions for even arguments.
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2
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1, 8, 2, 1, 0, 1, 7, 4, 5, 1, 4, 9, 9, 2, 9, 2, 3, 9, 0, 4, 0, 6, 7, 2, 5, 1, 3, 2, 2, 2, 6, 0, 0, 6, 8, 4, 8, 5, 7, 8, 2, 6, 8, 0, 2, 8, 6, 4, 8, 2, 7, 1, 7, 5, 5, 0, 0, 2, 0, 9, 3, 8, 0, 0, 2, 8, 6, 0, 6, 5, 8, 8, 6, 7, 7, 0, 5, 4, 8, 8, 9, 3, 6, 3, 9, 6, 0, 2, 4, 9, 7, 5, 2, 1, 4, 5, 2, 9, 7, 6, 6, 1, 0, 9, 9
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..105.
Bernd C. Kellner, On asymptotic constants related to products of Bernoulli numbers and factorials, arXiv:math/0604505.
Eric Weisstein's World of Mathematics, Abelian group.
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FORMULA
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Decimal expansion of zeta(2)*zeta(4)*...*zeta(2k)*...
If u(k) denotes the number of Abelian groups with group order k, then prod(k>=1, zeta(2*k))=sum(k>=1, u(k)/k^2). - Benoit Cloitre, Jun 25 2003
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EXAMPLE
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The value to 39 decimal places (calculated by Mathematica) is 1.82101745149929239040672513222600684857...
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MATHEMATICA
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RealDigits[Product[Zeta[2n], {n, 500}], 10, 110][[1]] (* Harvey P. Dale, Jan 31 2012 *)
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CROSSREFS
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Cf. A021002, A080730.
Sequence in context: A098829 A190404 A243433 * A262080 A164800 A011008
Adjacent sequences: A080726 A080727 A080728 * A080730 A080731 A080732
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KEYWORD
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cons,nonn
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AUTHOR
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Deepak R. N (deepak_rn(AT)safe-mail.net), Mar 08 2003
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EXTENSIONS
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More terms from Benoit Cloitre, Mar 08 2003
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STATUS
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approved
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