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%I #26 May 09 2020 00:25:06
%S 1,16,1296,20736,12960000,4320000,10372320000,165957120000,
%T 40327580160000,8065516032000,118087220224512000,118087220224512000,
%U 3372689096832287232000,3372689096832287232000,16863445484161436160000,269815127746582978560000,22535229284522356952309760000
%N Denominator of Sum_{k=1..n} (-1)^(k+1)/k^4.
%C Lim_{n -> infinity} A120296(n)/a(n) = A267315 = (7/8)*A013662.
%e The first few fractions are 1, 15/16, 1231/1296, 19615/20736, 12280111/12960000, 4090037/4320000, 9824498837/10372320000, ... = A120296/A334585.
%p b := proc(n) local k: add((-1)^(k + 1)/k^4, k = 1 .. n): end proc:
%p seq(denom(b(n)), n = 1 .. 17);
%t Denominator @ Accumulate[Table[(-1)^(k + 1)/k^4, {k, 1, 17}]] (* _Amiram Eldar_, May 08 2020 *)
%o (PARI) a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^4)); \\ _Michel Marcus_, May 07 2020
%Y Cf. A013662, A120296 (numerators), A267315.
%K nonn,frac
%O 1,2
%A _Petros Hadjicostas_, May 06 2020