A280034 Numerators of fractions converging to limiting value of Fekete polynomials.

1, 5, 19, 3469, 21565, 7760593, 12478099, 643983856759, 32151685807, 29631345749270231, 7838095210258393229, 2803900612868369530799, 4374668242116396309035353, 17739652125936605409894015449, 113561057125598699175157226801, 33146519052882978854962342279401371

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] // Numerator, {k, 1, 16}] (* Jean-François Alcover, Sep 06 2018 *)

Crossrefs

Cf. A280035. Related to central column of array in A280033.

Sequence in context: A270477 A279256 A174490 * A270486 A278562 A013531

Adjacent sequences: A280031 A280032 A280033 * A280035 A280036 A280037

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 28 2016

Extensions

More terms from Lars Blomberg, Jun 14 2017

Status

approved