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 A333925 #8 Sep 06 2020 06:41:50 %S A333925 1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,1,0,1,1,1,0,1,0,1,1,1,0,0,1,0,1,1,2,1, %T A333925 1,0,1,0,1,1,2,1,2,0,0,1,0,1,1,2,2,3,1,1,0,1,0,1,1,2,2,3,2,2,0,0,1,0, %U A333925 1,1,2,2,4,3,4,2,1,0,1,0,1,1,2,2,4,3,5,3,2,0,0,1,0,1,1,2,2,4,4,6,5,5,2,1,0 %N A333925 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j=2..k+1} 1/(1 - x^j). %C A333925 A(n,k) is the number of partitions of n into parts 2, 3, ..., k and k + 1. %H A333925 David A. Corneth, <a href="/A333925/b333925.txt">Table of n, a(n) for n = 0..10010</a> (first 141 rows antidiagonals flattened) %H A333925 <a href="/index/Mo#Molien">Index entries for Molien series</a> %F A333925 G.f. of column k: Product_{j=2..k+1} 1/(1 - x^j). %e A333925 Square array begins: %e A333925 1, 1, 1, 1, 1, 1, ... %e A333925 0, 0, 0, 0, 0, 0, ... %e A333925 0, 1, 1, 1, 1, 1, ... %e A333925 0, 0, 1, 1, 1, 1, ... %e A333925 0, 1, 1, 2, 2, 2, ... %e A333925 0, 0, 1, 1, 2, 2, ... %t A333925 Table[Function[k, SeriesCoefficient[Product[1/(1 - x^j), {j, 2, k + 1}], {x, 0, n}]][i - n], {i, 0, 13}, {n, 0, i}] // Flatten %Y A333925 Columns k=0..12 give A000007, A059841, A103221, A266755, A008667, A037145, A001996, A266776, A266777, A266778, A266779, A266780, A266781. %Y A333925 Main diagonal gives A002865. %Y A333925 Cf. A008284, A058398. %K A333925 nonn,tabl %O A333925 0,33 %A A333925 _Ilya Gutkovskiy_, Apr 10 2020