A354064 Product_{n>=1} 1 / (1 - x^(2*n))^(a(n)/(2*n)!) = cosh(x).

1, -8, -104, 1408, -354944, 47546368, -6204652544, 68669145088, -47215125069824, 159504062197792768, -51085990673656315904, -6994033618612756938752, -15510963121850795776016384, 14479308135716773591282352128, 7469518701197092988127633473536, 11962377309169877924807975108608

Offset: 1

Author

Ilya Gutkovskiy, May 16 2022

Keywords

• sign

Crossrefs

Cf. A353609, A354055, A354056, A354063, A354065, A354066.

Programs

Mathematica

nmax = 32; Take[CoefficientList[Series[Sum[MoebiusMu[k] Log[Cosh[x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}] // Rest

Formula

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