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Search: id:A111922
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| A111922 |
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Numerator of x(n) = Sum((odd part of k)/(k^5): 1<=k<=n). |
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+0
6
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| 1, 33, 2705, 86641, 54233569, 18084523, 43438219723, 1390063548011, 337834614646673, 337850745678737, 4946795388123668417, 4946852336050088417, 141291773058735555757937, 141293528936024618797937
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Denominator of x(n) = A111923(n);
x(n) = a(n)/A111923(n) -> (Pi^4)/93 = 30*zeta(4)/31.
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REFERENCES
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G. Polya and G. Szego, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.
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LINKS
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Eric Weisstein's World of Mathematics, Odd Part
Eric Weisstein's World of Mathematics, Riemann Zeta Function
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EXAMPLE
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a(20) = 16405158877294964819100166210727563,
A111923(20) = 15663005949803936428703787909120000:
x(20)=a(20)/A111923(20)=1.04738..., x(20)*31/30=1.08229....
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CROSSREFS
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Cf. A000265, A013662, A111929, A111918, A111920.
Sequence in context: A120288 A099370 A118641 this_sequence A136541 A114071 A057981
Adjacent sequences: A111919 A111920 A111921 this_sequence A111923 A111924 A111925
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KEYWORD
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nonn,frac
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 21 2005
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