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%I #16 May 07 2021 05:09:11
%S 1,-1,0,2,-1,1,-5,11,-17,26,-36,35,-22,19,-67,219,-480,687,-469,-573,
%T 2508,-4785,6370,-6445,5235,-4543,8681,-26815,75043,-173159,334721,
%U -563200,876876,-1363232,2208921,-3621971,5631540,-7897299,9738858,-10479294,9989646,-9350820
%N Expansion of Product_{k>=1} (1 - (x*(1 - x))^k).
%F G.f.: exp(-Sum_{k>=1} sigma(k)*(x*(1-x))^k/k).
%t m = 41; CoefficientList[Series[Product[(1 - (x*(1 - x))^k), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 07 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, 1-(x*(1-x))^k))
%o (PARI) N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, sigma(k)*(x*(1-x))^k/k)))
%Y Convolution inverse of A307500.
%Y Cf. A307310, A307501.
%K sign
%O 0,4
%A _Seiichi Manyama_, Sep 21 2019