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A290695
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).
6
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, 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, 3, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,5
COMMENTS
See A290694 for comments.
FORMULA
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.
EXAMPLE
Triangle starts:
[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, 7]
[1, 1, 2, 1, 2, 1, 1, 1, 1]
MAPLE
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;
MATHEMATICA
T[n_] := Denominator[CoefficientList[Sum[(-1)^(n-j+1) StirlingS2[n, j-1] (j-1)! x^j/j, {j, 1, n+1}], x]];
Table[T[n], {n, 0, 7}] (* Jean-François Alcover, Jun 15 2019, from Maple *)
KEYWORD
nonn,tabf,frac
AUTHOR
Peter Luschny, Aug 24 2017
STATUS
approved