This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334582 #35 Jul 13 2023 16:29:06
%S A334582 1,8,216,1728,216000,216000,74088000,592704000,16003008000,
%T A334582 16003008000,21300003648000,21300003648000,46796108014656000,
%U A334582 6685158287808000,6685158287808000,53481266302464000,262753461344005632000,262753461344005632000
%N A334582 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^3.
%C A334582 For n = 1 to n = 13, a(n) = A195506(n), but a(14) = 6685158287808000 <> 46796108014656000 = A195506(14).
%C A334582 Lim_{n -> infinity} A136675(n)/a(n) = A197070.
%H A334582 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet eta function</a>.
%e A334582 The first few fractions are 1, 7/8, 197/216, 1549/1728, 195353/216000, 194353/216000, 66879079/74088000, 533875007/592704000, ... = A136675/A334582.
%p A334582 b := proc(n) local k: add((-1)^(k + 1)/k^3, k = 1 .. n): end proc:
%p A334582 seq(denom(b(n)), n=1..30);
%t A334582 Denominator @ Accumulate[Table[(-1)^(k + 1)/k^3, {k, 1, 18}]] (* _Amiram Eldar_, May 08 2020 *)
%o A334582 (PARI) a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^3)); \\ _Michel Marcus_, May 07 2020
%Y A334582 Cf. A136675 (numerators), A195506, A197070.
%K A334582 nonn,frac
%O A334582 1,2
%A A334582 _Petros Hadjicostas_, May 06 2020
%E A334582 Offset changed to 1 by _Georg Fischer_, Jul 13 2023