cp's OEIS Frontend

A119731 f-Pascal's triangle where f(n) = n^3 = A000578(n).

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