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 A290429 #22 Feb 16 2025 08:33:49
%S A290429 1,1,0,1,1,0,1,2,0,0,1,3,1,0,0,1,4,3,0,1,0,1,5,6,1,2,0,0,1,6,10,4,3,2,
%T A290429 0,0,1,7,15,10,5,6,0,0,0,1,8,21,20,10,12,3,0,0,0,1,9,28,35,21,21,12,0,
%U A290429 1,0,0,1,10,36,56,42,36,30,4,3,0,1,0,1,11,45,84,78,63,61,20,6,3,2,0,0,1,12,55,120,135,112,112,60,15,12,3,2,0,0
%N A290429 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of (Sum_{j>=0} x^(j*(j+1)*(j+2)/6))^k.
%C A290429 A(n,k) is the number of ways of writing n as a sum of k tetrahedral (or triangular pyramidal) numbers (A000292).
%H A290429 Seiichi Manyama, <a href="/A290429/b290429.txt">Antidiagonals n = 0..139, flattened</a>
%H A290429 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H A290429 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F A290429 G.f. of column k: (Sum_{j>=0} x^(j*(j+1)*(j+2)/6))^k.
%e A290429 Square array begins:
%e A290429 1, 1, 1, 1, 1, 1, ...
%e A290429 0, 1, 2, 3, 4, 5, ...
%e A290429 0, 0, 1, 3, 6, 10, ...
%e A290429 0, 0, 0, 1, 4, 10, ...
%e A290429 0, 1, 2, 3, 5, 10, ...
%e A290429 0, 0, 2, 6, 12, 21, ...
%t A290429 Table[Function[k, SeriesCoefficient[Sum[x^(i (i + 1) (i + 2)/6), {i, 0, n}]^k, {x, 0, n}]][j - n], {j, 0, 13}, {n, 0, j}] // Flatten
%Y A290429 Cf. A000292, A104246, A286180, A290054, A290430.
%Y A290429 Cf. A000007 (column 0), A023533 (column 1), A282172 (column 5).
%Y A290429 Main diagonal gives A303170.
%Y A290429 Similar to, but different from, A045847.
%K A290429 nonn,tabl
%O A290429 0,8
%A A290429 _Ilya Gutkovskiy_, Jul 31 2017