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 A354173 #6 May 22 2022 08:54:45 %S A354173 -1,-8,104,-12032,354944,47546368,6204652544,-6174957043712, %T A354173 47215125069824,159504062197792768,51085990673656315904, %U A354173 54592541528151763714048,15510963121850795776016384,14479308135716773591282352128,-7469518701197092988127633473536,-77646018400552596699424746364731392 %N A354173 Product_{n>=1} (1 + x^(2*n))^(a(n)/(2*n)!) = cos(x). %F A354173 E.g.f.: Sum_{k>=1} A067856(k) * log(cos(x^k)) / k (even powers only). %t A354173 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = {1, 0, -1, 0}[[Mod[n + 1, 4, 1]]]/n! - b[n, n - 1]; a[n_] := (2 n)! c[2 n]; Table[a[n], {n, 1, 16}] %Y A354173 Cf. A067856, A170912, A170913, A354063, A354171, A354172, A354174, A354175, A354176. %K A354173 sign %O A354173 1,2 %A A354173 _Ilya Gutkovskiy_, May 18 2022