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%I #11 Aug 26 2017 08:22:27
%S 1,1,1,1,1,3,1,1,1,3,1,5,1,1,1,3,1,5,1,7,1,1,1,3,1,5,1,7,1,1,1,1,1,3,
%T 1,1,1,7,1,1,1,11,1,1,1,3,1,5,1,7,1,1,1,11,1,13,1,1,1,3,1,5,1,1,1,1,1,
%U 11,1,13,1,1,1,1,1,3,1,5,1,1,1,1,1,11,1,13,1,1
%N Triangle read by rows, denominators of coefficients (in rising powers) of rational polynomials P(n,x) such that Integral_{x=0..1} P'(n,x) = BernoulliMedian(n).
%C See A291447 and A290694 for comments.
%F T(n,k) = Denominator([x^k] Integral(Sum_{j=0..n}(-1)^(n-j)*Stirling2(n,j)*j!*x^j)^m) for m = 2, n >= 0 and k = 0..m*n+1.
%e Triangle starts:
%e [1, 1]
%e [1, 1, 1, 3]
%e [1, 1, 1, 3, 1, 5]
%e [1, 1, 1, 3, 1, 5, 1, 7]
%e [1, 1, 1, 3, 1, 5, 1, 7, 1, 1]
%e [1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 11]
%e [1, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 11, 1, 13]
%p # See A291447.
%t T[n_] := Integrate[Sum[(-1)^(n-j+1) StirlingS2[n, j] j! x^j, {j,0,n}]^2, x];
%t Trow[n_] := CoefficientList[T[n], x] // Denominator;
%t Table[Trow[r], {r, 0, 7}] // Flatten
%Y Cf. A164555/A027642, A212196/A181131, A291449/A291450, A290694/A290695, A291447/A291448.
%K nonn,tabf,frac
%O 0,6
%A _Peter Luschny_, Aug 24 2017
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