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 A288580 #18 Apr 05 2020 09:34:10
%S A288580 1,1,-1,1,-1,4,1,1,-4,-36,1,1,-2,9,576,1,1,-4,-9,64,-14400,1,1,2,-3,
%T A288580 -8,-225,518400,1,1,2,-6,-16,40,-2304,-25401600,1,1,2,-9,-4,-15,324,
%U A288580 11025,1625702400,1,1,2,3,-8,-25,144,280,147456,-131681894400,1,1,2,3,-12,-5,-24,105,-2240,-893025,13168189440000
%N A288580 Array read by upwards antidiagonals: T(n,k) = Product_{ 0 < |n-k*i| <= n} (n-k*i), with n >= 0, k >= 1.
%D A288580 F. Smarandache, Back and Forth Factorials, Arizona State Univ., Special Collections, 1972.
%H A288580 J. Dezert, ed., <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert.htm">Smarandacheials (1)</a>, Mathematics Magazine for Grades 1-12, No. 4, 2004.
%H A288580 J. Dezert, ed., <a href="http://www.mathematicsmagazine.com/corresp/J_Dezert/JDezert2.htm">Smarandacheials (2)</a>, Mathematics Magazine for Grades 1-12, No. 4, 2004.
%e A288580 Array begins:
%e A288580 1, -1, 4, -36, 576, -14400, 518400, -25401600, 1625702400, -131681894400, ...
%e A288580 1, -1, -4, 9, 64, -225, -2304, 11025, 147456, -893025, -14745600, 108056025, ...
%e A288580 1, 1, -2, -9, -8, 40, 324, 280, -2240, -26244, -22400, 246400, 3779136, ...
%e A288580 1, 1, -4, -3, -16, -15, 144, 105, 1024, 945, -14400, -10395, -147456, ...
%e A288580 1, 1, 2, -6, -4, -25, -24, -42, 336, 216, 2500, 2376, 4032, ...
%e A288580 1, 1, 2, -9, -8, -5, -36, -35, -64, 729, 640, 385, 5184, ...
%e A288580 1, 1, 2, 3, -12, -10, -6, -49, -48, -90, -120, 1320, 1080, ...
%e A288580 1, 1, 2, 3, -16, -15, -12, -7, -64, -63, -120, -165, 2304, ...
%e A288580 1, 1, 2, 3, 4, -20, -18, -14, -8, -81, -80, -154, -216, ...
%e A288580 1, 1, 2, 3, 4, -25, -24, -21, -16, -9, -100, -99, -192, ...
%e A288580 ...
%p A288580 T:=proc(n,k) local i,p;
%p A288580 p:=1;
%p A288580 for i from 0 to floor(2*n/k) do
%p A288580 if n-k*i <> 0 then p:=p*(n-k*i) fi; od:
%p A288580 p;
%p A288580 end;
%p A288580 scan1:=proc(a,M1) local lis,n,k; lis:=[]; for n from 1 to M1 do for k from 0 to n-1 do
%p A288580 lis:=[op(lis),a(k,n-k)]; od: od: lis; end:
%p A288580 scan1(T,12);
%t A288580 T[n_, k_] := Module[{i, p = 1}, For[i = 0, i <= Floor[2n/k], i++, If[n - k i != 0, p *= (n - k i)]]; p]; T[_, 0] = 1;
%t A288580 Table[T[k, n - k + 1], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 05 2020, after Maple *)
%Y A288580 Rows k=1 through 9 are signed A001044 or A092396, signed A184877 or A092397, A092398, A092399, A092971, A092972, A092973, A092974,
%K A288580 sign,tabl
%O A288580 0,6
%A A288580 _N. J. A. Sloane_, Jul 03 2017