A354173 Product_{n>=1} (1 + x^(2*n))^(a(n)/(2*n)!) = cos(x).

-1, -8, 104, -12032, 354944, 47546368, 6204652544, -6174957043712, 47215125069824, 159504062197792768, 51085990673656315904, 54592541528151763714048, 15510963121850795776016384, 14479308135716773591282352128, -7469518701197092988127633473536, -77646018400552596699424746364731392

Offset: 1

Author

Ilya Gutkovskiy, May 18 2022

Keywords

• sign

Crossrefs

Cf. A067856, A170912, A170913, A354063, A354171, A354172, A354174, A354175, A354176.

Programs

Mathematica

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}]

Formula

E.g.f.: Sum_{k>=1} A067856(k) * log(cos(x^k)) / k (even powers only).