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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, 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
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
KEYWORD
nonn,tabl,less
AUTHOR
Roger L. Bagula, Feb 19 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 26 2021
STATUS
approved