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A319862
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Triangle read by rows, 0 <= k <= n: T(n,k) is the denominator of the k-th Bernstein basis polynomial of degree n evaluated at the interval midpoint t = 1/2; numerator is A319861.
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4
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1, 2, 2, 4, 2, 4, 8, 8, 8, 8, 16, 4, 8, 4, 16, 32, 32, 16, 16, 32, 32, 64, 32, 64, 16, 64, 32, 64, 128, 128, 128, 128, 128, 128, 128, 128, 256, 32, 64, 32, 128, 32, 64, 32, 256, 512, 512, 128, 128, 256, 256, 128, 128, 512, 512, 1024, 512, 1024, 128, 512, 256, 512, 128, 1024, 512, 1024
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n, k) = denominator of binomial(n,k)/2^n.
A319862(n, k)/T(n, k) = binomial(n,k)/2^n.
T(n, n-k) = T(n, k).
T(n, 0) = 2^n.
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EXAMPLE
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Triangle begins:
1;
2, 2;
4, 2, 4;
8, 8, 8, 8;
16, 4, 8, 4, 16;
32, 32, 16, 16, 32, 32;
64, 32, 64, 16, 64, 32, 64;
128, 128, 128, 128, 128, 128, 128, 128;
256, 32, 64, 32, 128, 32, 64, 32, 256;
512, 512, 128, 128, 256, 256, 128, 128, 512, 512;
...
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MAPLE
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a:=(n, k)->2^n/gcd(binomial(n, k), 2^n): seq(seq(a(n, k), k=0..n), n=0..11); # Muniru A Asiru, Sep 30 2018
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MATHEMATICA
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T[n_, k_] = 2^n/GCD[Binomial[n, k], 2^n];
tabl[nn_] = TableForm[Table[T[n, k], {n, 0, nn}, {k, 0, n}]];
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PROG
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(Maxima)
T(n, k) := 2^n/gcd(binomial(n, k), 2^n)$
tabl(nn) := for n:0 thru nn do print(makelist(T(n, k), k, 0, n))$
(GAP) Flat(List([0..11], n->List([0..n], k->2^n/Gcd(Binomial(n, k), 2^n)))); # Muniru A Asiru, Sep 30 2018
(Sage)
def A319862(n, k): return denominator(binomial(n, k)/2^n)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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