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 A382532 #20 Apr 01 2025 09:33:42
%S A382532 1,1,6,105,3640,208845,17873856,2131900225,337767408000,
%T A382532 68586144251625,17361688356812800,5359035747797893161,
%U A382532 1980990543353657472000,863884504344556052483125,438824910158909833337856000,256841080519120696725634418625,171586094900260237697765926076416
%N A382532 a(n) = Product_{k=1..n} (n*k-k+1).
%C A382532 Fill an n X n square array with the numbers 1..n^2 in increasing order by rows. a(n) is the product of the numbers along the main antidiagonal (see example).
%F A382532 a(n) = (n-1)^n * Pochhammer(n/(n-1), n) for n>=2.
%F A382532 a(n) = Product_{k=1..n} A081493(n,k).
%F A382532 a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n+1). - _Vaclav Kotesovec_, Apr 01 2025
%e A382532 [1 2 3 4 5]
%e A382532 [1 2 3 4] [6 7 8 9 10]
%e A382532 [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e A382532 [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e A382532 [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e A382532 ------------------------------------------------------------------------
%e A382532 n 1 2 3 4 5
%e A382532 ------------------------------------------------------------------------
%e A382532 a(n) 1 6 105 3640 208845
%t A382532 Table[Product[n*k - k + 1, {k, n}], {n, 0, 20}]
%Y A382532 Row products of A081493.
%Y A382532 Cf. A006003, A370753.
%K A382532 nonn
%O A382532 0,3
%A A382532 _Wesley Ivan Hurt_, Mar 30 2025