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 A319862 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. 4
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened American Mathematical Society, From Bézier to Bernstein Rita T. Farouki, The Bernstein polynomial basis: A centennial retrospective, Computer Aided Geometric Design Vol. 29 (2012), 379-419. Ron Goldman, Pyramid Algorithms. A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling, Morgan Kaufmann Publishers, 2002, Chap. 5. Eric Weisstein's World of Mathematics, Bernstein Polynomial Wikipedia, Bernstein polynomial FORMULA T(n, k) = denominator of binomial(n,k)/2^n. T(n, k) = 2^n/A082907(n,k). A319862(n, k)/T(n, k) = binomial(n,k)/2^n. T(n, n-k) = T(n, k). T(n, 0) = 2^n. T(n, 1) = A075101(n). EXAMPLE 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;   ... MAPLE 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 MATHEMATICA T[n_, k_] = 2^n/GCD[Binomial[n, k], 2^n]; tabl[nn_] = TableForm[Table[T[n, k], {n, 0, nn}, {k, 0, n}]]; PROG (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) flatten([[A319862(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 20 2021 CROSSREFS Cf. A007318, A082907, A128433, A128434, A319861. Sequence in context: A217839 A083779 A045865 * A220977 A054134 A319822 Adjacent sequences:  A319859 A319860 A319861 * A319863 A319864 A319865 KEYWORD nonn,easy,frac,tabl AUTHOR Franck Maminirina Ramaharo, Sep 29 2018 STATUS approved

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Last modified January 18 16:56 EST 2022. Contains 350455 sequences. (Running on oeis4.)