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 A292477 #20 Sep 27 2020 12:30:14 %S A292477 1,1,2,1,2,4,1,2,3,6,1,2,3,5,10,1,2,3,4,7,14,1,2,3,4,6,9,20,1,2,3,4,5, %T A292477 8,12,26,1,2,3,4,5,7,10,15,36,1,2,3,4,5,6,9,12,18,46,1,2,3,4,5,6,8,11, %U A292477 15,23,60,1,2,3,4,5,6,7,10,13,18,28,74,1,2,3,4,5,6,7,9,12,15,21,33,94 %N A292477 Square array A(n,k), n >= 0, k >= 2, read by antidiagonals: A(n,k) = [x^(k*n)] Product_{j>=0} 1/(1 - x^(k^j)). %C A292477 A(n,k) is the number of partitions of k*n into powers of k. %H A292477 Seiichi Manyama, <a href="/A292477/b292477.txt">Antidiagonals n = 0..139, flattened</a> %H A292477 George E. Andrews, Aviezri S. Fraenkel, James A. Sellers, <a href="https://doi.org/10.4169/amer.math.monthly.122.9.880">Characterizing the number of m-ary partitions modulo m</a>, Amer. Math. Monthly 122:9 (2015), 880-885. %H A292477 <a href="/index/Par#part">Index entries for related partition-counting sequences</a> %e A292477 Square array begins: %e A292477 1, 1, 1, 1, 1, 1, ... %e A292477 2, 2, 2, 2, 2, 2, ... %e A292477 4, 3, 3, 3, 3, 3, ... %e A292477 6, 5, 4, 4, 4, 4, ... %e A292477 10, 7, 6, 5, 5, 5, ... %e A292477 14, 9, 8, 7, 6, 6, ... %t A292477 Table[Function[k, SeriesCoefficient[Product[1/(1 - x^k^i), {i, 0, n}], {x, 0, k n}]][j - n + 2], {j, 0, 12}, {n, 0, j}] // Flatten %Y A292477 Columns k=2..5 give A000123, A005704, A005705, A005706. %Y A292477 Mirror of A089688 (excluding the first row). %Y A292477 Cf. A145515, A294316. %K A292477 nonn,tabl %O A292477 0,3 %A A292477 _Ilya Gutkovskiy_, Sep 17 2017