A111922 Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^5)).

1, 33, 2705, 86641, 54233569, 18084523, 43438219723, 1390063548011, 337834614646673, 337850745678737, 4946795388123668417, 4946852336050088417, 141291773058735555757937, 141293528936024618797937

Offset: 1

Author

Reinhard Zumkeller, Aug 21 2005

Keywords

• nonn
• frac

Comments

Denominator of x(n) = A111923(n);

x(n) = a(n)/A111923(n) -> (Pi^4)/93 = 30*zeta(4)/31.

Examples

			a(20) = 16405158877294964819100166210727563,
A111923(20) = 15663005949803936428703787909120000:
x(20) = a(20)/A111923(20) = 1.04738..., x(20)*31/30=1.08229....
		

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

• Eric Weisstein's World of Mathematics, Odd Part
• Eric Weisstein's World of Mathematics, Riemann Zeta Function

Crossrefs

Cf. A000265, A013662, A111929, A111918, A111920, A111923.