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 A320824 #17 Sep 08 2022 08:46:23
%S A320824 1,6,6,90,720,90,1680,45360,45360,1680,34650,2217600,7484400,2217600,
%T A320824 34650,756756,94594500,756756000,756756000,94594500,756756,17153136,
%U A320824 3705077376,57891834000,137225088000,57891834000,3705077376,17153136
%N A320824 T(n, k) = (m*n)!/(k!*(n-k)!)^m with m = 3; triangle read by rows, 0 <= k <= n.
%H A320824 G. C. Greubel, <a href="/A320824/b320824.txt">Rows n=0..100 of triangle, flattened</a>
%F A320824 T(n, k) = ((3*n)!/(n!)^3) * binomial(n, k)^3 = A006480(n)*A181543(n, k).
%e A320824 Triangle starts:
%e A320824 [0] 1;
%e A320824 [1] 6, 6;
%e A320824 [2] 90, 720, 90;
%e A320824 [3] 1680, 45360, 45360, 1680;
%e A320824 [4] 34650, 2217600, 7484400, 2217600, 34650;
%e A320824 [5] 756756, 94594500, 756756000, 756756000, 94594500, 756756;
%p A320824 T := (n, k, m) -> (m*n)!/(k!*(n-k)!)^m:
%p A320824 seq(seq(T(n, k, 3), k=0..n), n=0..7);
%t A320824 Table[((3*n)!/(n!)^3)*Binomial[n, k]^3, {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Oct 27 2018 *)
%o A320824 (PARI) t(n, k) = (3*n)!/(k!*(n-k)!)^3
%o A320824 trianglerows(n) = for(x=0, n-1, for(y=0, x, print1(t(x, y), ", ")); print(""))
%o A320824 /* Print initial 6 rows of triangle as follows: */
%o A320824 trianglerows(6) \\ _Felix Fröhlich_, Oct 21 2018
%o A320824 (Magma) [[(Factorial(3*n)/(Factorial(n))^3)*Binomial(n, k)^3: k in [0..n]]: n in [0..15]]; // _G. C. Greubel_, Oct 27 2018
%o A320824 (GAP) Flat(List([0..6],n->List([0..n],k->Factorial(3*n)/(Factorial(k)*Factorial(n-k))^3))); # _Muniru A Asiru_, Oct 27 2018
%Y A320824 Cf. A007318 (Pascal, m=1), A069466 (m=2), this sequence (m=3).
%Y A320824 Cf. A006480, A181543.
%K A320824 nonn,tabl
%O A320824 0,2
%A A320824 _Peter Luschny_, Oct 21 2018