A334585 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^4.

1, 16, 1296, 20736, 12960000, 4320000, 10372320000, 165957120000, 40327580160000, 8065516032000, 118087220224512000, 118087220224512000, 3372689096832287232000, 3372689096832287232000, 16863445484161436160000, 269815127746582978560000, 22535229284522356952309760000

Offset

1,2

Comments

Lim_{n -> infinity} A120296(n)/a(n) = A267315 = (7/8)*A013662.

Links

Table of n, a(n) for n=1..17.

Example

The first few fractions are 1, 15/16, 1231/1296, 19615/20736, 12280111/12960000, 4090037/4320000, 9824498837/10372320000, ... = A120296/A334585.

Maple

b := proc(n) local k: add((-1)^(k + 1)/k^4, k = 1 .. n): end proc:
seq(denom(b(n)), n = 1 .. 17);

Mathematica

Denominator @ Accumulate[Table[(-1)^(k + 1)/k^4, {k, 1, 17}]] (* Amiram Eldar, May 08 2020 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^4)); \\ Michel Marcus, May 07 2020

Crossrefs

Cf. A013662, A120296 (numerators), A267315.

Sequence in context: A072161 A173544 A248619 * A163929 A072914 A007480

Adjacent sequences: A334582 A334583 A334584 * A334586 A334587 A334588

Keyword

nonn,frac

Author

Petros Hadjicostas, May 06 2020

Status

approved