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%I #7 Mar 27 2019 10:03:44
%S 1,-2,2,-4,32,-128,496,-2336,29312,-395776,3194624,-21951488,
%T 277270528,-4027191296,38850203648,-739834458112,19460560584704,
%U -299971773661184,3169121209090048,-51853341314514944,1234704403684130816,-30653318499154788352,658369600764729884672,-10809496145754051313664
%N Expansion of e.g.f. Product_{k>=1} ((1 - x^k)/(1 + x^k))^(1/k).
%F E.g.f.: exp(-2*Sum_{k>=1} A001227(k)*x^k/k).
%F E.g.f.: exp(-Sum_{k>=1} A054844(k)*x^k/k).
%p a:=series(mul(((1-x^k)/(1+x^k))^(1/k),k=1..100),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 23; CoefficientList[Series[Product[((1 - x^k)/(1 + x^k))^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 23; CoefficientList[Series[Exp[-2 Sum[Total[Mod[Divisors[k], 2] x^k]/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A001227, A028342, A028343, A054844, A156616, A168243, A285675, A294356, A295792.
%K sign
%O 0,2
%A _Ilya Gutkovskiy_, Dec 03 2017
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