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 A382672 #15 Apr 08 2025 18:20:15
%S A382672 0,2,17,450,35472,12127741
%N A382672 Number of integer solutions to Product_{k=1..n} (3 + c(k)) = 3 * Product_{k=1..n} c(k) with 0 < c(k) <= c(k+1).
%e A382672 For n=3, a(3) = 17 because 3*x*y*z = (x + 3)*(y + 3)*(z + 3), 0 < x <= y <= z has 17 positive integer solutions: {{2,16,285}, {2,17,150}, {2,18,105}, {2,20,69}, {2,21,60}, {2,24,45}, {2,25,42}, {2,30,33}, {3,7,60}, {3,8,33}, {3,9,24}, {3,12,15}, {4,5,42}, {4,6,21}, {4,7,15}, {5,6,12}, {6,6,9}}.
%t A382672 a[n_]:=(p=c/@Range[n];Length@Solve[3 Times@@p==Times@@(3+p)&&LessEqual@@Flatten[{0,p}],p,Integers]);Array[a,5]
%Y A382672 Cf. A263207, A375787, A380749, A381644.
%K A382672 nonn,more
%O A382672 1,2
%A A382672 _Zhining Yang_, Apr 03 2025