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Denominator of Sum_{k=1..n} (-1)^(k+1)/k^6.
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%I #23 May 07 2020 22:14:40

%S 1,64,46656,2985984,46656000000,5184000000,609892416000000,

%T 39033114624000000,256096265048064000000,256096265048064000000,

%U 453690155404813307904000000,453690155404813307904000000,2189875725319351517910798336000000

%N Denominator of Sum_{k=1..n} (-1)^(k+1)/k^6.

%C Lim_{n -> infinity} A136677(n)/a(n) = A275703 = (31/32)*A013664.

%e The first few fractions are: 1, 63/64, 45991/46656, 2942695/2985984, 45982595359/46656000000, 5109066151/5184000000, ... = A136677/A334605.

%t Denominator @ Accumulate[Table[(-1)^(k + 1)/k^6, {k, 1, 13}]] (* _Amiram Eldar_, May 07 2020 *)

%o (PARI) a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^6)); \\ _Michel Marcus_, May 07 2020

%Y Cf. A013664, A136677 (numerators), A275703.

%K nonn,frac

%O 1,2

%A _Petros Hadjicostas_, May 07 2020