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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-Fran├žois 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 A088198 A318288

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 August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)