A280033 - OEIS

%I #15 Sep 06 2018 11:10:32

%S 1,-2,10,-2,16,-184,456,-184,16,-272,5776,-30736,55504,-30736,5776,

%T -272,7936,-284288,2555008,-8998016,13801600,-8998016,2555008,-284288,

%U 7936,-353792,20594432,-280444416,1567885056,-4267790592,5960135424,-4267790592,1567885056,-280444416,20594432,-353792

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

%H Lars Blomberg, <a href="/A280033/b280033.txt">Table of n, a(n) for n = 1..625</a> (The first 25 rows)

%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. See Cor. 2.6.

%e Initial rows are:

%e 1,

%e -2,10,-2,

%e 16,-184,456,-184,16,

%e -272,5776,-30736,55504,-30736,5776,-272,

%e 7936,-284288,2555008,-8998016,13801600,-8998016,2555008,-284288,7936,

%e ...

%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[2k-1, 2j-1] T[j], {j, 1, k-1}];

%t 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;

%t Table[(2k-1)! F[k, m], {k, 1, 6}, {m, 1, 2k-1}] // Flatten (* _Jean-François Alcover_, Sep 06 2018 *)

%Y Cf. A280034, A280035.

%K sign,tabf

%O 1,2

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

%E More terms from _Lars Blomberg_, Jun 14 2017