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 A302020 #6 Feb 16 2025 08:33:53
%S A302020 1,1,2,5,12,28,66,156,367,863,2031,4779,11244,26456,62248,146462,
%T A302020 344608,810822,1907769,4488757,10561519,24850017,58469179,137571128,
%U A302020 323688747,761601701,1791959579,4216270956,9920391613,23341519267,54919860316,129219997322,304039515247,715369360371
%N A302020 Expansion of 1/(1 - x*Product_{k>=1} (1 + x^(2*k))/(1 - x^(2*k-1))).
%H A302020 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A302020 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionb.html">Partition Function b_k</a>
%F A302020 G.f.: 1/(1 - x*Product_{k>=1} (1 - x^(4*k))/(1 - x^k)).
%F A302020 G.f.: 1/(1 - x*Product_{k>=1} (1 + x^k + x^(2*k) + x^(3*k))).
%F A302020 a(0) = 1; a(n) = Sum_{k=1..n} A001935(k-1)*a(n-k).
%t A302020 nmax = 33; CoefficientList[Series[1/(1 - x Product[(1 + x^(2 k))/(1 - x^(2 k - 1)), {k, 1, nmax}]), {x, 0, nmax}], x]
%t A302020 nmax = 33; CoefficientList[Series[1/(1 + (1 - x) QPochhammer[-1, x^2]/(2 QPochhammer[1/x, x^2])), {x, 0, nmax}], x]
%t A302020 nmax = 33; CoefficientList[Series[1/(1 - x EllipticTheta[2, 0, x]/(Sqrt[2] x^(1/8) EllipticTheta[2, Pi/4, Sqrt[x]])), {x, 0, nmax}], x]
%Y A302020 Antidiagonal sums of A296068.
%Y A302020 Cf. A001935, A299106, A299108.
%K A302020 nonn
%O A302020 0,3
%A A302020 _Ilya Gutkovskiy_, Mar 30 2018