This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307500 #11 Oct 31 2020 02:53:54
%S A307500 1,1,1,-1,-2,-4,3,-1,17,-16,21,-57,67,-130,305,-536,995,-1726,2652,
%T A307500 -4286,7320,-13043,24458,-45405,81415,-141724,239755,-400603,676872,
%U A307500 -1171076,2072334,-3695550,6519951,-11279015,19188230,-32462795,55334284,-95718737,167673672,-294894076
%N A307500 Expansion of Product_{k>=1} 1/(1 - (x*(1 - x))^k).
%H A307500 Seiichi Manyama, <a href="/A307500/b307500.txt">Table of n, a(n) for n = 0..1000</a>
%F A307500 G.f.: exp(Sum_{k>=1} sigma(k)*(x*(1 - x))^k/k).
%F A307500 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(k,n-k)*A000041(k).
%t A307500 nmax = 39; CoefficientList[Series[Product[1/(1 - (x (1 - x))^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A307500 nmax = 39; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] (x (1 - x))^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]
%t A307500 Table[Sum[(-1)^(n - k) Binomial[k, n - k] PartitionsP[k], {k, 0, n}], {n, 0, 39}]
%Y A307500 Cf. A000041, A030528, A218482, A238441, A286955, A307501.
%K A307500 sign
%O A307500 0,5
%A A307500 _Ilya Gutkovskiy_, Apr 11 2019