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

%I #6 May 17 2022 07:25:35

%S 1,-2,-1,4,-19,164,-659,1408,-18775,642224,-3578279,-21642752,

%T -476298835,11904106304,25626362581,68669145088,-20903398375855,

%U 212840905389824,-6399968826052559,-78465506362130432,1010700510694925525,101465632831736751104,-1123931378903214542099

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

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

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

%Y Cf. A170914, A170915, A328186, A328191, A353607, A353873, A354056, A354063, A354064, A354065, A354066.

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, May 16 2022