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 A296067 #8 May 10 2018 23:07:18
%S A296067 1,1,0,1,1,0,1,2,-1,0,1,3,-1,0,0,1,4,0,-2,1,0,1,5,2,-5,3,0,0,1,6,5,-8,
%T A296067 3,2,-1,0,1,7,9,-10,-1,9,-4,-1,0,1,8,14,-10,-10,20,-7,-4,2,0,1,9,20,
%U A296067 -7,-24,31,-2,-15,5,1,0,1,10,27,0,-42,36,20,-40,9,8,-2,0,1,11,35,12,-62,28,65,-75,3,27,-8,-1,0
%N A296067 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} ((1 + x^(2*j-1))/(1 + x^(2*j)))^k.
%H A296067 G. C. Greubel, <a href="/A296067/b296067.txt">Rows n=0..100 of antidiagonals, flattened</a>
%F A296067 G.f. of column k: Product_{j>=1} ((1 + x^(2*j-1))/(1 + x^(2*j)))^k.
%F A296067 G.f. of column k: (x^(1/8)*theta_2(sqrt(x))/theta_2(x))^k, where theta_() is the Jacobi theta function.
%e A296067 G.f. of column k: A_k(x) = 1 + k*x + (1/2)*k*(k - 3)*x^2 + (1/6)*k*(k^2 - 9*k + 8)*x^3 + (1/24)*k*(k^3 - 18*k^2 + 59*k - 18)*x^4 + (1/120)*k*(k^4 - 30*k^3 + 215*k^2 - 330*k + 144)*x^5 + ...
%e A296067 Square array begins:
%e A296067 1, 1, 1, 1, 1, 1, ...
%e A296067 0, 1, 2, 3, 4, 5, ...
%e A296067 0, -1, -1, 0, 2, 5, ...
%e A296067 0, 0, -2, -5, -8, -10, ...
%e A296067 0, 1, 3, 3, -1, -10, ...
%e A296067 0, 0, 2, 9, 20, 31, ...
%t A296067 Table[Function[k, SeriesCoefficient[Product[((1 + x^(2 i - 1))/(1 + x^(2 i)))^k, {i, 1, n}], {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
%t A296067 Table[Function[k, SeriesCoefficient[(x^(1/8) EllipticTheta[2, 0, x^(1/2)]/EllipticTheta[2, 0, x])^k, {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
%Y A296067 Columns k=0..8 give A000007, A029838, A029839, A029840, A029841, A029842, A029843, A029844, A029845 (with offset 0).
%Y A296067 Main diagonal gives A296043.
%Y A296067 Cf. A296068.
%K A296067 sign,tabl
%O A296067 0,8
%A A296067 _Ilya Gutkovskiy_, Dec 04 2017