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 A383223 #5 Apr 27 2025 05:56:54
%S A383223 0,2,15,375,28901,5185573
%N A383223 Number of integer solutions to Product_{k=1..n} (4 + c(k)) = 4 * Product_{k=1..n} c(k) with 0 < c(k) <= c(k+1).
%e A383223 For n=3, a(3) = 15 because 4*x*y*z = (x + 4)*(y + 4)*(z + 4), 0 < x <= y <= z has 15 positive integer solutions: {{2,13,204}, {2,14,108}, {2,15,76}, {2,16,60}, {2,18,44}, {2,20,36}, {2,24,28}, {3,6,140}, {3,7,44}, {3,8,28}, {3,12,14}, {4,5,36}, {4,6,20}, {4,8,12}, {5,6,12}}.
%t A383223 a[n_]:=(p=c/@Range[n]; Length@Solve[4 Times@@p==Times@@(4+p)&&LessEqual@@Flatten[{0, p}], p, Integers]); Array[a, 5]
%Y A383223 Cf. A263207, A375787, A380749, A381644, A382672.
%K A383223 nonn,more
%O A383223 1,2
%A A383223 _Zhining Yang_, Apr 19 2025