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 A289522 #9 Mar 29 2019 15:51:20
%S A289522 1,1,0,1,2,0,1,4,2,0,1,6,8,4,0,1,8,18,16,6,0,1,10,32,44,32,8,0,1,12,
%T A289522 50,96,102,56,12,0,1,14,72,180,256,216,96,16,0,1,16,98,304,550,624,
%U A289522 428,160,22,0,1,18,128,476,1056,1512,1408,816,256,30,0,1,20,162,704,1862,3240,3820,3008,1494,404,40,0
%N A289522 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=0} ((1 + x^(2*j+1))/(1 - x^(2*j+1)))^k.
%F A289522 G.f. of column k: Product_{j>=0} ((1 + x^(2*j+1))/(1 - x^(2*j+1)))^k.
%F A289522 G.f. of column 2k: (theta_3(x)/theta_4(x))^k, where theta_() is the Jacobi theta function.
%F A289522 For asymptotics of column k see comment from _Vaclav Kotesovec_ in A261648.
%e A289522 Square array begins:
%e A289522 1, 1, 1, 1, 1, 1, ...
%e A289522 0, 2, 4, 6, 8, 10, ...
%e A289522 0, 2, 8, 18, 32, 50, ...
%e A289522 0, 4, 16, 44, 96, 180, ...
%e A289522 0, 6, 32, 102, 256, 550, ...
%e A289522 0, 8, 56, 216, 624, 1512, ...
%t A289522 Table[Function[k, SeriesCoefficient[Product[((1 + x^(2 i + 1))/(1 - x^(2 i + 1)))^k, {i, 0, n}], {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
%t A289522 Table[Function[k, SeriesCoefficient[(QPochhammer[-x, x^2]/QPochhammer[x, x^2])^k, {x, 0, n}]][j - n], {j, 0, 11}, {n, 0, j}] // Flatten
%Y A289522 Columns k=0-6 give: A000007, A080054, A007096, A261647, A014969, A261648, A014970.
%Y A289522 Rows n=0-3 give: A000012, A005843, A001105, A217873.
%Y A289522 Main diagonal gives A291697.
%K A289522 nonn,tabl
%O A289522 0,5
%A A289522 _Ilya Gutkovskiy_, Jul 07 2017