%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