A111920 Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4)).

1, 17, 475, 7627, 960287, 962287, 330928441, 5296012681, 143167958387, 143231970419, 190769776691689, 190794429473689, 419345761582878733, 419413977483774733, 16780996063666453, 268499592964601893

Offset

1,2

Comments

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

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

References

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

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Odd Part

Eric Weisstein's World of Mathematics, Apery's constant

Eric Weisstein's World of Mathematics, Riemann Zeta Function

Example

a(35) = 6357636538031086038114593391432155018318189,
A111921(35) = 5668063317569576031821812156438757376000000:
x(35) = a(35)/A111921(35) = 1.12165..., x(35)*15/14=1.20177....

Crossrefs

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

Sequence in context: A196717 A220598 A239926 * A296740 A166116 A173148

Adjacent sequences: A111917 A111918 A111919 * A111921 A111922 A111923

Keyword

nonn,frac

Author

Reinhard Zumkeller, Aug 21 2005

Status

approved