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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS See A290694 for comments. LINKS Table of n, a(n) for n=0..89. 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 *) CROSSREFS Cf. A164555/A027642, A212196/A181131, A291449/A291450, A290694/A290695, A291447/A291448. Sequence in context: A106796 A265743 A082850 * A277446 A334029 A334297 Adjacent sequences: A290692 A290693 A290694 * A290696 A290697 A290698 KEYWORD nonn,tabf,frac AUTHOR Peter Luschny, Aug 24 2017 STATUS approved

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Last modified April 24 03:03 EDT 2024. Contains 371917 sequences. (Running on oeis4.)