A280037 Denominators of fractions converging to limiting value of Galois polynomials.

1, 3, 5, 21, 1512, 15120, 30888, 16216200, 11762150400, 482718652416, 685679904000, 597828484915200, 2690228182118400000, 269791454835302400000, 191686828660482355200000, 25892338511873433600000, 129800853740753466163200000, 4685378150528730950270976000000

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] // Denominator, {k, 1, 18}] (* Jean-François Alcover, Sep 06 2018 *)

Crossrefs

Cf. A280036. Related to central column of array in A280040.

Sequence in context: A153889 A364576 A186751 * A292557 A147442 A370580

Adjacent sequences: A280034 A280035 A280036 * A280038 A280039 A280040

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 28 2016

Extensions

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

Status

approved