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A280034 Numerators of fractions converging to limiting value of Fekete polynomials. 3
1, 5, 19, 3469, 21565, 7760593, 12478099, 643983856759, 32151685807, 29631345749270231, 7838095210258393229, 2803900612868369530799, 4374668242116396309035353, 17739652125936605409894015449, 113561057125598699175157226801, 33146519052882978854962342279401371 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 11:57 EDT 2021. Contains 343882 sequences. (Running on oeis4.)