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