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 A336163 #37 Jul 11 2020 07:33:33
%S A336163 1,1,1,1,2,1,1,3,10,1,1,4,21,56,1,1,5,34,171,346,1,1,6,49,352,1521,
%T A336163 2252,1,1,7,66,605,3946,14283,15184,1,1,8,85,936,8065,46744,138909,
%U A336163 104960,1,1,9,106,1351,14346,113525,573616,1385163,739162,1,1,10,129,1856,23281,231876,1656145,7217536,14072193,5280932,1
%N A336163 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j * binomial(n,j)^3.
%C A336163 Column k is the diagonal of the rational function 1 / (1 + y + z + x*y + y*z + k*z*x + (k+1)*x*y*z).
%C A336163 Column k is the diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - k*x*y*z).
%e A336163 Square array begins:
%e A336163 1, 1, 1, 1, 1, 1, ...
%e A336163 1, 2, 3, 4, 5, 6, ...
%e A336163 1, 10, 21, 34, 49, 66, ...
%e A336163 1, 56, 171, 352, 605, 936, ...
%e A336163 1, 346, 1521, 3946, 8065, 14346, ...
%e A336163 1, 2252, 14283, 46744, 113525, 231876, ...
%t A336163 Unprotect[Power]; 0^0 = 1; T[n_, k_] := Sum[k^j * Binomial[n, j]^3, {j, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Jul 11 2020 *)
%Y A336163 Columns k=0-6 give: A000012, A000172, A206178, A206180, A216483, A216636, A216698.
%Y A336163 Main diagonal gives A241247.
%Y A336163 Cf. A307883, A336179, A336187.
%K A336163 nonn,tabl
%O A336163 0,5
%A A336163 _Seiichi Manyama_, Jul 10 2020