A354065 Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + tan(x).

1, -2, 2, -8, 56, -496, 3184, -22784, 273920, -4539136, 48104704, -506000384, 10591523840, -204528633856, 2888557717504, -53417657237504, 1249919350046720, -28453501844586496, 624022403933077504, -13729309300086800384, 372737701735949926400, -11010228423219933085696

Offset: 1

Author

Ilya Gutkovskiy, May 16 2022

Keywords

• sign

Crossrefs

Cf. A000182, A003707, A009006, A353583, A353584, A353611, A353911, A354055, A354056, A354063, A354064, A354066.

Programs

Mathematica

nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + Tan[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 + tan(x^k)) / k.