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A173475
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Triangle T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = Product_{j=0..n} A051179(j), read by rows.
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1
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = Product_{j,0,n} A051179(j).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 5, 1;
1, 85, 85, 1;
1, 21845, 371365, 21845, 1;
1, 1431655765, 6254904037285, 6254904037285, 1431655765, 1;
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MATHEMATICA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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