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Denominator of Sum_{k=1..n} (-1)^(k+1)/k^5.
3

%I #19 May 09 2020 00:26:17

%S 1,32,7776,248832,777600000,777600000,13069123200000,418211942400000,

%T 101625502003200000,101625502003200000,16366888723117363200000,

%U 16366888723117363200000,6076911214672415134617600000

%N Denominator of Sum_{k=1..n} (-1)^(k+1)/k^5.

%C Lim_{n -> infinity} A136676(n)/a(n) = A267316 = (15/16)*A013663.

%e The first few fractions are 1, 31/32, 7565/7776, 241837/248832, 755989457/777600000, 755889457/777600000, ... = A136676/A334604.

%t Denominator @ Accumulate[Table[(-1)^(k + 1)/k^5, {k, 1, 13}]] (* _Amiram Eldar_, May 08 2020 *)

%o (PARI) a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^5)); \\ _Michel Marcus_, May 07 2020

%Y Cf. A013663, A136676 (numerators), A267316.

%K nonn

%O 1,2

%A _Petros Hadjicostas_, May 07 2020