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

1, 1, 1, 1, 2, 1, 1, 9, 9, 1, 1, 730, 1458, 730, 1, 1, 389017001, 3488380912, 3488380912, 389017001, 1, 1, 58871587162270593034051002, 42508286068210633669596761529, 84898828962096726153125421056, 42508286068210633669596761529, 58871587162270593034051002, 1

Offset: 0

Author

Philippe Deléham, Jun 14 2006

Keywords

• nonn
• tabl

Examples

			Triangle begins;
  1;
  1,         1;
  1,         2,          1;
  1,         9,          9,          1;
  1,       730,       1458,        730,         1;
  1, 389017001, 3488380912, 3488380912, 389017001, 1;
		

Links

• G. C. Greubel, Rows n = 0..9 of the triangle, flattened

Crossrefs

Cf. A000578, A007318.

Programs

Mathematica

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]];
Table[T[n, k], {n, 0, 7}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 19 2021 *)

Sage

@CachedFunction
def T(n,k):
    if (k<0 or k>n): return 0
    elif (k==0): return 1
    else: return T(n-1, k)^3 + T(n-1, k-1)^3
flatten([[T(n,k) for k in (0..n)] for n in (0..7)]) # G. C. Greubel, Jul 19 2021

Formula

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.