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

Author

Petros Hadjicostas, May 06 2020

Keywords

• nonn
• frac

Comments

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

Examples

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

Crossrefs

Cf. A013662, A120296 (numerators), A267315.

Programs

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 *)

PARI

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