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A280034 Numerators of fractions converging to limiting value of Fekete polynomials. 3

%I #11 Sep 06 2018 11:10:41

%S 1,5,19,3469,21565,7760593,12478099,643983856759,32151685807,

%T 29631345749270231,7838095210258393229,2803900612868369530799,

%U 4374668242116396309035353,17739652125936605409894015449,113561057125598699175157226801,33146519052882978854962342279401371

%N Numerators of fractions converging to limiting value of Fekete polynomials.

%H Lars Blomberg, <a href="/A280034/b280034.txt">Table of n, a(n) for n = 1..25</a>

%H Christian Günther, Kai-Uwe Schmidt, <a href="http://arxiv.org/abs/1602.01750">L^q norms of Fekete and related polynomials</a>, arXiv:1602.01750 [math.NT], 2016

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

%t (* "gen" stands for "generalized Eulerian number" *)

%t gen[n_, x_] := Sum[(-1)^j Binomial[n + 1, j] (x + 1 - j)^n, {j, 0, Floor[x + 1]}];

%t T[k_] := T[k] = 1 - Sum[Binomial[2 k - 1, 2 j - 1] T[j], {j, 1, k - 1}];

%t 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;

%t Table[F[k, k] // Numerator, {k, 1, 16}] (* _Jean-François Alcover_, Sep 06 2018 *)

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

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, Dec 28 2016

%E More terms from _Lars Blomberg_, Jun 14 2017

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)