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%I #10 Apr 03 2019 03:00:39
%S 1,1,1,2,5,12,27,58,122,257,549,1190,2600,5683,12367,26749,57530,
%T 123202,263115,561131,1196248,2550975,5443115,11620526,24814735,
%U 52979512,113038103,240936717,512916683,1090501249,2315608462,4911611864,10408318627,22040127864
%N Expansion of Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).
%C First differences of the binomial transform of A000700.
%F G.f.: Product_{k>=1} (1 + x^(2*k-1)/(1 - x)^(2*k-1)).
%F a(n) ~ 2^(n-2) * exp(Pi*sqrt(n/3)/2 + Pi^2/96) / (3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 01 2019
%p a:=series(mul(1/(1+(-x)^k/(1-x)^k),k=1..50),x=0,34): seq(coeff(a,x,n),n=0..33); # _Paolo P. Lava_, Apr 02 2019
%t nmax = 33; CoefficientList[Series[Product[1/(1 + (-x)^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000700, A129519, A218482, A307264.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Apr 01 2019
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