A280035 Denominators of fractions converging to limiting value of Fekete polynomials.

1, 3, 5, 315, 567, 51975, 19305, 212837625, 2127125, 371231385525, 17717861581875, 1095751306274625, 284473896821296875, 185436341599368234375, 184915818535229656875, 8168656283793770092453125, 5285601124807733589234375, 5940428375270025028345078125

Offset

1,2

Links

Lars Blomberg, Table of n, a(n) for n = 1..25

Christian Günther, Kai-Uwe Schmidt, L^q norms of Fekete and related polynomials, arXiv:1602.01750 [math.NT], 2016

Example

1/1, 5/3, 19/5, 3469/315, 21565/567, 7760593/51975, 12478099/19305, 643983856759/212837625,

Mathematica

(* "gen" stands for "generalized Eulerian number" *)
gen[n_, x_] := Sum[(-1)^j Binomial[n + 1, j] (x + 1 - j)^n, {j, 0, Floor[x + 1]}];
T[k_] := T[k] = 1 - Sum[Binomial[2 k - 1, 2 j - 1] T[j], {j, 1, k - 1}];
F[0, 0] = 1; F[k_, m_] /; 1 <= m <= 2 k - 1 := F[k, m] = Sum[Binomial[2 k - 1, 2 j - 1] T[j]/(2 j - 1)! Sum[gen[2 j - 1, i - 1] F[k - j, m - i], {i, 0, m}], {j, 1, k}]; F[_, _] = 0;
Table[F[k, k] // Denominator, {k, 1, 18}] (* Jean-François Alcover, Sep 06 2018 *)

Crossrefs

Cf. A280034. Related to central column of array in A280033.

Sequence in context: A232239 A087368 A309740 * A087670 A271390 A138584

Adjacent sequences: A280032 A280033 A280034 * A280036 A280037 A280038

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 28 2016

Extensions

More terms from Lars Blomberg, Jun 14 2017

Status

approved