A280033 Irregular triangle read by rows: numbers (2n-1)!*F(n,m) related to Fekete polynomials.

1, -2, 10, -2, 16, -184, 456, -184, 16, -272, 5776, -30736, 55504, -30736, 5776, -272, 7936, -284288, 2555008, -8998016, 13801600, -8998016, 2555008, -284288, 7936, -353792, 20594432, -280444416, 1567885056, -4267790592, 5960135424, -4267790592, 1567885056, -280444416, 20594432, -353792

Offset

1,2

Links

Lars Blomberg, Table of n, a(n) for n = 1..625 (The first 25 rows)

Christian Günther, Kai-Uwe Schmidt, L^q norms of Fekete and related polynomials, arXiv:1602.01750 [math.NT], 2016. See Cor. 2.6.

Example

Initial rows are:
1,
-2,10,-2,
16,-184,456,-184,16,
-272,5776,-30736,55504,-30736,5776,-272,
7936,-284288,2555008,-8998016,13801600,-8998016,2555008,-284288,7936,
...

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[2k-1, 2j-1] T[j], {j, 1, k-1}];
F[0, 0] = 1; F[k_, m_] /; 1 <= m <= 2k-1 := F[k, m] = Sum[Binomial[2k-1, 2j - 1] T[j]/(2j-1)! Sum[gen[2j-1, i-1] F[k-j, m-i], {i, 0, m}], {j, 1, k}]; F[_, _] = 0;
Table[(2k-1)! F[k, m], {k, 1, 6}, {m, 1, 2k-1}] // Flatten (* Jean-François Alcover, Sep 06 2018 *)

Crossrefs

Cf. A280034, A280035.

Sequence in context: A221551 A010700 A121521 * A347096 A346239 A188635

Adjacent sequences: A280030 A280031 A280032 * A280034 A280035 A280036

Keyword

sign,tabf

Author

N. J. A. Sloane, Dec 28 2016

Extensions

More terms from Lars Blomberg, Jun 14 2017

Status

approved