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 A320354 #5 Mar 29 2019 15:51:20
%S A320354 1,1,0,1,1,0,1,2,3,0,1,3,16,21,0,1,4,45,416,315,0,1,5,96,2835,33280,
%T A320354 9765,0,1,6,175,11904,722925,8053760,615195,0,1,7,288,37625,7428096,
%U A320354 739552275,5863137280,78129765,0,1,8,441,98496,48724375,23205371904,3028466566125,12816818094080,19923090075,0
%N A320354 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals: A(n,k) = Product_{j=1..n} (k^j - 1).
%F A320354 G.f. of column k: Sum_{i>=0} k^(i*(i+1)/2)*x^i / Product_{j=0..i} (1 + k^j*x).
%F A320354 For asymptotics of column k see comment from _Vaclav Kotesovec_ in A027880.
%e A320354 Square array begins:
%e A320354 1, 1, 1, 1, 1, 1, ...
%e A320354 0, 1, 2, 3, 4, 5, ...
%e A320354 0, 3, 16, 45, 96, 175, ...
%e A320354 0, 21, 416, 2835, 11904, 37625, ...
%e A320354 0, 315, 33280, 722925, 7428096, 48724375, ...
%e A320354 0, 9765, 8053760, 739552275, 23205371904, 378832015625, ...
%t A320354 Table[Function[k, Product[k^j - 1, {j, 1, n}]][m - n + 1], {m, 0, 9}, {n, 0, m}] // Flatten
%t A320354 Table[Function[k, SeriesCoefficient[Sum[k^(i (i + 1)/2) x^i/Product[(1 + k^j x), {j, 0, i}], {i, 0, n}], {x, 0, n}]][m - n + 1], {m, 0, 9}, {n, 0, m}] // Flatten
%Y A320354 Columns k=1..12 give A000007, A005329, A027871, A027637, A027872, A027873, A027875, A027876, A027877, A027878, A027879, A027880.
%Y A320354 Cf. A069777, A225816.
%K A320354 nonn,tabl
%O A320354 0,8
%A A320354 _Ilya Gutkovskiy_, Oct 11 2018