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Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4)).
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%I #10 Dec 25 2019 08:34:27

%S 1,17,475,7627,960287,962287,330928441,5296012681,143167958387,

%T 143231970419,190769776691689,190794429473689,419345761582878733,

%U 419413977483774733,16780996063666453,268499592964601893

%N Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4)).

%C Denominator of x(n) = A111921(n);

%C x(n) = a(n)/A111921(n) -> 14*zeta(3)/15.

%D G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddPart.html">Odd Part</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AperysConstant.html">Apery's constant</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunction.html">Riemann Zeta Function</a>

%e a(35) = 6357636538031086038114593391432155018318189,

%e A111921(35) = 5668063317569576031821812156438757376000000:

%e x(35) = a(35)/A111921(35) = 1.12165..., x(35)*15/14=1.20177....

%Y Cf. A000265, A002117, A111929, A111918, A111921, A111922.

%K nonn,frac

%O 1,2

%A _Reinhard Zumkeller_, Aug 21 2005