A173507 Triangle T(n, k, q) = 2*c(n, q)/(c(k,q)*c(n-k,q)) where c(n,q) = Product_{j=0..n} (q^(q^j) - 1) and q=3, read by rows.

1, 1, 1, 1, 757, 1, 1, 293292210961, 293292210961, 1, 1, 17054864932424529613394216562274995877, 6607739819910193062857078382087289676159166721, 17054864932424529613394216562274995877, 1

Offset: 0

Author

Roger L. Bagula, Feb 20 2010

Keywords

• nonn
• tabl
• easy
• less

Examples

			The triangle begins as:
  1;
  1,            1;
  1,          757,            1;
  1, 293292210961, 293292210961, 1;
		

Links

• G. C. Greubel, Rows n = 0..7 of the triangle, flattened

Programs

Mathematica

c[n_, q_]:= Product[q^(q^j) -1, {j,0,n}];
T[n_, k_, q_]:= 2*c[n, q]/(c[k, q]*c[n-k, q]);
Table[T[n, k, 3], {n, 0, 6}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 25 2021 *)

Sage

@CachedFunction
def c(n,q): return product(q^(q^j) -1 for j in (0..n))
def T(n,k,q): return 2*c(n,q)/(c(k,q)*c(n-k,q))
flatten([[T(n,k,3) for k in (0..n)] for n in (0..6)]) # G. C. Greubel, Apr 25 2021

Formula

T(n, k, q) = 2*c(n, q)/(c(k,q)*c(n-k,q)) where c(n,q) = Product_{j=0..n} (q^(q^j) - 1) and q=3.

Extensions

Edited by G. C. Greubel, Apr 25 2021