A290695 - OEIS

%I #16 Jun 15 2019 10:31:56

%S 1,1,1,1,2,1,1,2,3,1,1,2,1,2,1,1,2,3,1,5,1,1,2,1,2,1,1,1,1,2,3,1,1,1,

%T 7,1,1,2,1,2,1,1,1,1,1,1,2,3,1,5,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,2,

%U 3,1,1,1,1,1,1,1,11,1,1,2,1,2,1,1,1,1,1,1,1,1

%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) = Bernoulli(n, 1).

%C See 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 = 1 and k = 0..n+1.

%e Triangle starts:

%e [1, 1]

%e [1, 1, 2]

%e [1, 1, 2, 3]

%e [1, 1, 2, 1, 2]

%e [1, 1, 2, 3, 1, 5]

%e [1, 1, 2, 1, 2, 1, 1]

%e [1, 1, 2, 3, 1, 1, 1, 7]

%e [1, 1, 2, 1, 2, 1, 1, 1, 1]

%p T_row := n -> denom(PolynomialTools:-CoefficientList(add((-1)^(n-j+1)*Stirling2(n, j-1)*(j-1)!*x^j/j, j=1..n+1), x)): for n from 0 to 7 do T_row(n) od;

%t T[n_] := Denominator[CoefficientList[Sum[(-1)^(n-j+1) StirlingS2[n, j-1] (j-1)! x^j/j, {j, 1, n+1}], x]];

%t Table[T[n], {n, 0, 7}] (* _Jean-François Alcover_, Jun 15 2019, from Maple *)

%Y Cf. A164555/A027642, A212196/A181131, A291449/A291450, A290694/A290695, A291447/A291448.

%K nonn,tabf,frac

%O 0,5

%A _Peter Luschny_, Aug 24 2017