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Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.
4

%I #21 May 09 2020 03:31:28

%S 1,4,36,144,3600,1200,58800,235200,6350400,6350400,768398400,

%T 768398400,129859329600,129859329600,129859329600,519437318400,

%U 150117385017600,50039128339200,18064125330451200,3612825066090240,3612825066090240,3612825066090240,1911184459961736960

%N Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.

%C For n = 1 to n = 19, we have a(n) = A068589(n), but a(20) = 3612825066090240 <> A068589(20) = 18064125330451200.

%e The first few fractions are 1, 3/4, 31/36, 115/144, 3019/3600, 973/1200, 48877/58800, 191833/235200, 5257891/6350400, 5194387/6350400, ... = A119682/A334580.

%p b := proc(n) local k: add((-1)^(k + 1)/k^2, k = 1 .. n): end proc:

%p seq(denom(b(n)), n=1..30);

%o (PARI) a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^2)); \\ _Michel Marcus_, May 07 2020

%Y Cf. A068589, A119682 (numerators).

%K nonn,frac

%O 1,2

%A _Petros Hadjicostas_, May 06 2020