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%I #13 Jul 20 2021 03:26:59
%S 1,1,1,1,2,1,1,9,9,1,1,730,1458,730,1,1,389017001,3488380912,
%T 3488380912,389017001,1,1,58871587162270593034051002,
%U 42508286068210633669596761529,84898828962096726153125421056,42508286068210633669596761529,58871587162270593034051002,1
%N f-Pascal's triangle where f(n) = n^3 = A000578(n).
%H G. C. Greubel, <a href="/A119731/b119731.txt">Rows n = 0..9 of the triangle, flattened</a>
%F T(n,k) = T(n-1,k-1)^3 + T(n-1,k)^3 ; T(0,0) = 1 ; T(n,k) = 0 if k<0 or if k>n.
%e Triangle begins;
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 9, 9, 1;
%e 1, 730, 1458, 730, 1;
%e 1, 389017001, 3488380912, 3488380912, 389017001, 1;
%t T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[k==0, 1, T[n-1, k]^3 + T[n-1, k-1]^3]];
%t Table[T[n, k], {n, 0, 7}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Jul 19 2021 *)
%o (Sage)
%o @CachedFunction
%o def T(n,k):
%o if (k<0 or k>n): return 0
%o elif (k==0): return 1
%o else: return T(n-1, k)^3 + T(n-1, k-1)^3
%o flatten([[T(n,k) for k in (0..n)] for n in (0..7)]) # _G. C. Greubel_, Jul 19 2021
%Y Cf. A000578, A007318.
%K nonn,tabl
%O 0,5
%A _Philippe Deléham_, Jun 14 2006
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