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%I #6 May 17 2022 07:25:46
%S 1,-8,-104,1408,-354944,47546368,-6204652544,68669145088,
%T -47215125069824,159504062197792768,-51085990673656315904,
%U -6994033618612756938752,-15510963121850795776016384,14479308135716773591282352128,7469518701197092988127633473536,11962377309169877924807975108608
%N Product_{n>=1} 1 / (1 - x^(2*n))^(a(n)/(2*n)!) = cosh(x).
%F E.g.f.: Sum_{k>=1} mu(k) * log(cosh(x^k)) / k (even powers only).
%t 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
%Y Cf. A353609, A354055, A354056, A354063, A354065, A354066.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, May 16 2022