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%I #34 May 15 2022 12:13:58
%S 1,-1,-1,1,-16,86,-526,302,-10424,323304,-2805408,-6563424,-374664720,
%T 5877455520,32949033168,-24011091024,-16610113920768,87369247685760,
%U -5110200130727808,-23241729685643136,1042965176555775744,49535245994720788224
%N Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 - log(1 - x).
%F Product_{n>=1} 1 / (1 - x^n)^(a(n)/n!) = 1 + Sum_{n>=1} x^n/n.
%F E.g.f.: Sum_{k>=1} mu(k) * log(1 - log(1 - x^k)) / k.
%t nmax = 22; CoefficientList[Series[Sum[MoebiusMu[k] Log[1 - Log[1 - x^k]]/k, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%Y Cf. A157159, A157164, A348205, A348206, A352404, A352664, A352691.
%K sign
%O 1,5
%A _Ilya Gutkovskiy_, May 15 2022