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

0,5

Links

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

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.

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A269934 A269898 A291864 * A101833 A261858 A068683

Adjacent sequences: A173504 A173505 A173506 * A173508 A173509 A173510

Keyword

nonn,tabl,easy,less

Author

Roger L. Bagula, Feb 20 2010

Extensions

Edited by G. C. Greubel, Apr 25 2021

Status

approved