This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319862 #21 Feb 16 2025 08:33:56
%S A319862 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,
%T A319862 64,128,128,128,128,128,128,128,128,256,32,64,32,128,32,64,32,256,512,
%U A319862 512,128,128,256,256,128,128,512,512,1024,512,1024,128,512,256,512,128,1024,512,1024
%N 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.
%H A319862 G. C. Greubel, <a href="/A319862/b319862.txt">Rows n = 0..50 of the triangle, flattened</a>
%H A319862 American Mathematical Society, <a href="http://www.ams.org/publicoutreach/feature-column/fcarc-bezier">From Bézier to Bernstein</a>
%H A319862 Rita T. Farouki, <a href="https://doi.org/10.1016/j.cagd.2012.03.001">The Bernstein polynomial basis: A centennial retrospective</a>, Computer Aided Geometric Design Vol. 29 (2012), 379-419.
%H A319862 Ron Goldman, <a href="https://doi.org/10.1016/B978-1-55860-354-7.X5000-4">Pyramid Algorithms. A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling</a>, Morgan Kaufmann Publishers, 2002, Chap. 5.
%H A319862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BernsteinPolynomial.html">Bernstein Polynomial</a>
%H A319862 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bernstein_polynomial">Bernstein polynomial</a>
%F A319862 T(n, k) = denominator of binomial(n,k)/2^n.
%F A319862 T(n, k) = 2^n/A082907(n,k).
%F A319862 A319862(n, k)/T(n, k) = binomial(n,k)/2^n.
%F A319862 T(n, n-k) = T(n, k).
%F A319862 T(n, 0) = 2^n.
%F A319862 T(n, 1) = A075101(n).
%e A319862 Triangle begins:
%e A319862 1;
%e A319862 2, 2;
%e A319862 4, 2, 4;
%e A319862 8, 8, 8, 8;
%e A319862 16, 4, 8, 4, 16;
%e A319862 32, 32, 16, 16, 32, 32;
%e A319862 64, 32, 64, 16, 64, 32, 64;
%e A319862 128, 128, 128, 128, 128, 128, 128, 128;
%e A319862 256, 32, 64, 32, 128, 32, 64, 32, 256;
%e A319862 512, 512, 128, 128, 256, 256, 128, 128, 512, 512;
%e A319862 ...
%p A319862 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
%t A319862 T[n_, k_] = 2^n/GCD[Binomial[n, k], 2^n];
%t A319862 tabl[nn_] = TableForm[Table[T[n, k], {n, 0, nn}, {k, 0, n}]];
%o A319862 (Maxima)
%o A319862 T(n, k) := 2^n/gcd(binomial(n, k), 2^n)$
%o A319862 tabl(nn) := for n:0 thru nn do print(makelist(T(n, k), k, 0, n))$
%o A319862 (GAP) Flat(List([0..11],n->List([0..n],k->2^n/Gcd(Binomial(n,k),2^n)))); # _Muniru A Asiru_, Sep 30 2018
%o A319862 (Sage)
%o A319862 def A319862(n,k): return denominator(binomial(n,k)/2^n)
%o A319862 flatten([[A319862(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jul 20 2021
%Y A319862 Cf. A007318, A082907, A128433, A128434, A319861.
%K A319862 nonn,easy,frac,tabl
%O A319862 0,2
%A A319862 _Franck Maminirina Ramaharo_, Sep 29 2018