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 A290430 #12 Feb 16 2025 08:33:49
%S A290430 1,1,0,1,1,0,1,2,0,0,1,3,1,0,0,1,4,3,0,0,0,1,5,6,1,0,1,0,1,6,10,4,0,2,
%T A290430 0,0,1,7,15,10,1,3,2,0,0,1,8,21,20,5,4,6,0,0,0,1,9,28,35,15,6,12,3,0,
%U A290430 0,0,1,10,36,56,35,12,20,12,0,0,0,0,1,11,45,84,70,28,31,30,4,0,1,0,0,1,12,55,120,126,64,49,60,20,0,3,0,0,0
%N A290430 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)*(2*j+1)/6))^k.
%C A290430 A(n,k) is the number of ways of writing n as a sum of k square pyramidal numbers (A000330).
%H A290430 Seiichi Manyama, <a href="/A290430/b290430.txt">Antidiagonals n = 0..139, flattened</a>
%H A290430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePyramidalNumber.html">Square Pyramidal Number</a>
%H A290430 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%F A290430 G.f. of column k: (Sum_{j>=0} x^(j*(j+1)*(2*j+1)/6))^k.
%e A290430 Square array begins:
%e A290430 1, 1, 1, 1, 1, 1, ...
%e A290430 0, 1, 2, 3, 4, 5, ...
%e A290430 0, 0, 1, 3, 6, 10, ...
%e A290430 0, 0, 0, 1, 4, 10, ...
%e A290430 0, 0, 0, 0, 1, 5, ...
%e A290430 0, 1, 2, 3, 4, 6, ...
%t A290430 Table[Function[k, SeriesCoefficient[Sum[x^(i (i + 1) (2 i + 1)/6), {i, 0, n}]^k, {x, 0, n}]][j - n], {j, 0, 13}, {n, 0, j}] // Flatten
%Y A290430 Cf. A000330, A045847, A122141, A286815, A290429.
%Y A290430 Cf. A000007 (column 0), A253903 (column 1), A282173 (column 6).
%Y A290430 Main diagonal gives A303172.
%K A290430 nonn,tabl
%O A290430 0,8
%A A290430 _Ilya Gutkovskiy_, Jul 31 2017