A280036 Numerators of fractions converging to limiting value of Galois polynomials.

1, 4, 11, 92, 15481, 411913, 2482927, 4181926481, 10431687390203, 1562251141547683, 8527085144590567, 29905005221325235087, 563972987813159419491869, 245998831704214345304467561, 786438313703834134845784743061, 493123210279233679062515691019

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, 4/3, 11/5, 92/21, 15481/1512, 411913/15120, 2482927/30888, 4181926481/16216200, ...

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]}];
c[k_] := c[k] = 1 - Sum[Binomial[k, j] Binomial[k - 1, j - 1] c[j], {j, 1, k - 1}];
G[0, 0] = 1; G[k_, m_] /; 1 <= m <= 2 k - 1 := G[k, m] = Sum[Binomial[k, j] Binomial[k - 1, j - 1] c[j]/(2 j - 1)! Sum[gen[2 j - 1, i - 1] G[k - j, m - i], {i, 0, m}], {j, 1, k}]; G[_, _] = 0;
Table[G[k, k] // Numerator, {k, 1, 16}] (* Jean-François Alcover, Sep 06 2018 *)

Crossrefs

Cf. A280037. Related to central column of array in A280040.

Sequence in context: A320289 A298858 A181267 * A125888 A266894 A296617

Adjacent sequences: A280033 A280034 A280035 * A280037 A280038 A280039

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 28 2016

Extensions

a(9) and beyond from Lars Blomberg, Jul 07 2017

Status

approved