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 A158887 #26 Jun 10 2025 03:23:56
%S A158887 1,1,4,45,1056,43225,2756160,253586025,31872332800,5252921480961,
%T A158887 1099886703552000,285322741626047125,89844523369696972800,
%U A158887 33764841634845724313625,14930493174337400252809216
%N A158887 a(n) = (n+1)^n * n! * binomial(n-1 + 1/(n+1), n).
%C A158887 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 diagonal, n > 0 (see example). - _Wesley Ivan Hurt_, May 16 2025
%H A158887 G. C. Greubel, <a href="/A158887/b158887.txt">Table of n, a(n) for n = 0..230</a>
%F A158887 a(n) = Product_{k=0..n-1} (k*(n+1) + 1) for n>0 with a(0)=1.
%F A158887 a(n) = coefficient of x^n/(n!*(n+1)^n) in 1/(1-x)^(1/(n+1)).
%F A158887 a(n) ~ sqrt(2*Pi) * exp(1-n) * n^(2*n-3/2). - _Vaclav Kotesovec_, Jun 28 2015
%F A158887 a(n) = (1+n)^n * gamma(n+1/(n+1)) / gamma(1/(n+1)). - _Gerry Martens_, May 30 2018
%e A158887 a(1) = 1, a(2) = 1*4, a(3) = 1*5*9, a(4) = 1*6*11*16, a(5) = 1*7*13*19*25.
%e A158887 From _Wesley Ivan Hurt_, May 16 2025: (Start)
%e A158887 [1 2 3 4 5]
%e A158887 [1 2 3 4] [6 7 8 9 10]
%e A158887 [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e A158887 [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e A158887 [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e A158887 ------------------------------------------------------------------------
%e A158887 n 1 2 3 4 5
%e A158887 ------------------------------------------------------------------------
%e A158887 a(n) 1 4 45 1056 43225
%e A158887 (End)
%p A158887 seq(mul(j*(n+1)+1, j=0..n-1), n = 0..15); # _G. C. Greubel_, Mar 04 2020
%t A158887 Table[(n+1)^n n!Binomial[n-1+1/(n+1),n],{n,0,20}] (* _Harvey P. Dale_, Oct 26 2011 *)
%t A158887 a[n_] := (1 + n)^n Gamma[n + 1/(1 + n)]/Gamma[1/(n + 1)] // FullSimplify
%t A158887 Table[a[n], {n, 0, 20}] (* _Gerry Martens_, May 30 2018 *)
%o A158887 (PARI) a(n)=(n+1)^n*n!*polcoeff(1/(1-x+x*O(x^n))^(1/(n+1)),n)
%o A158887 (PARI) a(n)=if(n==0,1,prod(k=0,n-1,k*(n+1)+1))
%o A158887 (Magma) [1] cat [&*[j*(n+1)+1: j in [0..n-1]]: n in [1..15]]; // _G. C. Greubel_, Mar 04 2020
%o A158887 (Sage) [product(j*(n+1)+1 for j in (0..n-1)) for n in (0..15)] # _G. C. Greubel_, Mar 04 2020
%o A158887 (GAP) List([0..15], n-> Product([0..n-1], j-> j*(n+1)+1) ); # _G. C. Greubel_, Mar 04 2020
%K A158887 nonn
%O A158887 0,3
%A A158887 _Paul D. Hanna_, May 01 2009