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Search: id:A164656
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| A164656 |
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Numerators of partial sums of Theta(5):=sum(1/(2*j-1)^5,j=1..infty). |
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3
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| 1, 244, 762743, 12820180976, 3115356499043, 501734380891571068, 186290962962179367466549, 186291207179611798681792, 264507060005034822095008296869, 654945930087597102815813733559637156, 654946089730308117005814730177159031, 4215458332009996232497953858159263996273008
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OFFSET
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1,2
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COMMENT
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The denominators are given by A164657.
Rationals (partial sums) Theta(5,n) := sum(1/(2*j-1)^5,j=1..n) (in lowest terms). The limit of these rationals is Theta(5)= (1-1/2^5)*Zeta(5) approximately 1.004523763 (Zeta(n) is the Euler, Riemann Zeta function).
This is a member of the k-family of rational sequences Theta(k,n):=sum(1/(2*j-1)^k,j=1..n), k>=1, which includes A025550/A025547 (but only for the first 38 entries), A120268/A128492, A164655(n)/A128507(n) (the denominators may depart for higher n values), A120269/A128493, a(n)/A164657, for k=1..5.
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REFERENCES
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R. Ayoub, Euler and the Zeta Function, Am. Math. Monthly 81 (1974) 1067-1086.
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LINKS
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W. Lang: Theta(k,n), k-family of rational sequences and limits.
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FORMULA
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a(n) = numer(Theta(5,n))= numerator(sum(1/(2*j-1)^5,j=1..n)), n>=1.
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EXAMPLE
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Rationals Theta(5,n): [1, 244/243, 762743/759375, 12820180976/12762815625, 3115356499043/3101364196875,...].
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CROSSREFS
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Sequence in context: A002594 A085440 A146552 this_sequence A013684 A157246 A129210
Adjacent sequences: A164653 A164654 A164655 this_sequence A164657 A164658 A164659
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang@physik.uni-karlsruhe.de) Oct 16 2009
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