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 A333144 #5 Apr 10 2020 14:39:55 %S A333144 1,1,1,2,1,1,6,1,1,2,2,24,1,1,1,2,2,6,120,1,1,1,2,2,1,6,6,4,24,720,1, %T A333144 1,1,2,1,1,6,2,2,2,24,6,12,120,5040,1,1,1,2,1,1,6,2,1,2,2,24,2,4,2,6, %U A333144 120,24,12,48,720,40320 %N A333144 Irregular triangle where row n lists the product of the factorials of the exponentials of the partitions of n and the partitions are enumerated in canonical order. %C A333144 By 'canonical order' we understand the graded reverse lexicographic order (the default order of Mathematica and SageMath). %e A333144 The irregular table starts: %e A333144 [0] [1] %e A333144 [1] [1] %e A333144 [2] [1, 2] %e A333144 [3] [1, 1, 6] %e A333144 [4] [1, 1, 2, 2, 24] %e A333144 [5] [1, 1, 1, 2, 2, 6, 120] %e A333144 [6] [1, 1, 1, 2, 2, 1, 6, 6, 4, 24, 720] %e A333144 [7] [1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 24, 6, 12, 120, 5040] %o A333144 (SageMath) %o A333144 def A333144row(n): %o A333144 return [product(factorial(expo) for expo in partition.to_exp()) for partition in Partitions(n)] %o A333144 for n in (0..9): print(A333144row(n)) %Y A333144 Row sums are A161779. %Y A333144 Cf. A069123. %K A333144 nonn,tabf %O A333144 0,4 %A A333144 _Peter Luschny_, Apr 10 2020