A334582 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^3.

1, 8, 216, 1728, 216000, 216000, 74088000, 592704000, 16003008000, 16003008000, 21300003648000, 21300003648000, 46796108014656000, 6685158287808000, 6685158287808000, 53481266302464000, 262753461344005632000, 262753461344005632000

Offset: 1

Author

Petros Hadjicostas, May 06 2020

Keywords

• nonn
• frac

Comments

For n = 1 to n = 13, a(n) = A195506(n), but a(14) = 6685158287808000 <> 46796108014656000 = A195506(14).

Lim_{n -> infinity} A136675(n)/a(n) = A197070.

Examples

			The first few fractions are 1, 7/8, 197/216, 1549/1728, 195353/216000, 194353/216000, 66879079/74088000, 533875007/592704000, ... = A136675/A334582.
		

Links

• Wikipedia, Dirichlet eta function.

Crossrefs

Cf. A136675 (numerators), A195506, A197070.

Programs

Maple

b := proc(n) local k: add((-1)^(k + 1)/k^3, k = 1 .. n): end proc:
seq(denom(b(n)), n=1..30);

Mathematica

Denominator @ Accumulate[Table[(-1)^(k + 1)/k^3, {k, 1, 18}]] (* Amiram Eldar, May 08 2020 *)

PARI

a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^3)); \\ Michel Marcus, May 07 2020

Extensions

Offset changed to 1 by Georg Fischer, Jul 13 2023