A173475 Triangle T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = Product_{j=0..n} A051179(j), read by rows.

1, 1, 1, 1, 5, 1, 1, 85, 85, 1, 1, 21845, 371365, 21845, 1, 1, 1431655765, 6254904037285, 6254904037285, 1431655765, 1, 1, 6148914691236517205, 1760625833240390967011987365, 452480839142780478522080752805, 1760625833240390967011987365, 6148914691236517205, 1

Offset

0,5

Links

G. C. Greubel, Rows n = 0..10 of the triangle, flattened

Formula

T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = Product_{j,0,n} A051179(j).

Example

Triangle begins as:
  1;
  1,          1;
  1,          5,             1;
  1,         85,            85,             1;
  1,      21845,        371365,         21845,          1;
  1, 1431655765, 6254904037285, 6254904037285, 1431655765, 1;

Mathematica

c[n_]:= Product[2^(2^j) - 1, {j, 0, n}];
T[n_, k_]:= c[n]/(c[k]*c[n-k]);
Table[T[n, k], {n, 0, 8}, {k, 0, n}]//Flatten

Prog

(Sage)
@CachedFunction
def c(n): return product( 2^(2^j) -1 for j in (0..n) )
def T(n, k): return c(n)/(c(k)*c(n-k))
flatten([[T(n, k) for k in (0..n)] for n in (0..8)]) # G. C. Greubel, Apr 26 2021

Crossrefs

Cf. A051179.

Sequence in context: A111820 A174912 A106238 * A174919 A156952 A158748

Adjacent sequences: A173472 A173473 A173474 * A173476 A173477 A173478

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Feb 19 2010

Extensions

Edited by G. C. Greubel, Apr 26 2021

Status

approved