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Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + tan(x).
7

%I #6 May 17 2022 07:25:50

%S 1,-2,2,-8,56,-496,3184,-22784,273920,-4539136,48104704,-506000384,

%T 10591523840,-204528633856,2888557717504,-53417657237504,

%U 1249919350046720,-28453501844586496,624022403933077504,-13729309300086800384,372737701735949926400,-11010228423219933085696

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

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

%t nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 + Tan[x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

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

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, May 16 2022