A354117 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + arctan(x).

1, -2, -2, 8, -16, 176, -832, 384, 8192, 447744, -4228608, -15860736, -398991360, 10938421248, 44581613568, -29064658944, -17762113880064, -18092698632192, -7331825098948608, -64037289416196096, 3154526750647517184, 91791873021766533120, -1278044473427380666368

Offset: 1

Author

Ilya Gutkovskiy, May 17 2022

Keywords

• sign

Crossrefs

Cf. A010050, A110708, A353820, A353915, A354065, A354115, A354116, A354118.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + ArcTan[x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

Formula

E.g.f.: Sum_{k>=1} mu(k) * log(1 + arctan(x^k)) / k.