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%I #7 Jul 20 2021 03:27:12
%S 1,1,1,1,2,1,1,9,9,1,1,64,8,64,1,1,625,625,625,625,1,1,7776,243,16,
%T 243,7776,1,1,117649,117649,117649,117649,117649,117649,1,1,2097152,
%U 16384,2097152,128,2097152,16384,2097152,1,1,43046721,43046721,6561,43046721,43046721,6561,43046721,43046721,1
%N Triangle, read by rows, T(n,k) = denominator of the maximum of the k-th Bernstein polynomial of degree n; numerator is A128433.
%H G. C. Greubel, <a href="/A128434/b128434.txt">Rows n = 0..50 of the triangle, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BernsteinPolynomial.html">Bernstein Polynomial</a>
%F A128433(n,k)/T(n,k) = binomial(n,k) * k^k * (n-k)^(n-k) / n^n.
%F For n>0: Sum_{k=0..n} A128433(n,k)/T(n,k) = A090878(n)/A036505(n-1);
%F T(n, n-k) = T(n,k).
%F T(n, 0) = T(n, n) = 1.
%F for n>0: A128433(n,1)/T(n,1) = A000312(n-1)/A000169(n).
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 9, 9, 1;
%e 1, 64, 8, 64, 1;
%e 1, 625, 625, 625, 625, 1;
%e 1, 7776 243, 16, 243, 7776, 1;
%e 1, 117649, 117649, 117649, 117649, 117649, 117649, 1;
%e 1, 2097152, 16384, 2097152, 128, 2097152, 16384, 2097152, 1;
%t B[n_, k_]:= If[k==0 || k==n, 1, Binomial[n, k]*k^k*(n-k)^(n-k)/n^n];
%t T[n_, k_]= Denominator[B[n, k]];
%t Table[T[n, k], {n,0,10}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jul 19 2021 *)
%o (Sage)
%o def B(n,k): return 1 if (k==0 or k==n) else binomial(n, k)*k^k*(n-k)^(n-k)/n^n
%o def T(n,k): return denominator(B(n,k))
%o flatten([[T(n,k) for k in (0..n)] for n in (0..10)]) # _G. C. Greubel_, Jul 19 2021
%Y Cf. A000169, A000312, A036505, A090878, A128433.
%K nonn,tabl,frac
%O 0,5
%A _Reinhard Zumkeller_, Mar 03 2007
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