A280040 Irregular triangle read by rows: numbers (2n-1)!*G(n,m) related to Galois polynomials.

1, -1, 8, -1, 4, -76, 264, -76, 4, -33, 1248, -9735, 22080, -9735, 1248, -33, 456, -32088, 440448, -2085096, 3715440, -2085096, 440448, -32088, 456, -9460, 1216600, -26297700, 205444800, -704121000, 1087450320, -704121000, 205444800, -26297700, 1216600, -9460

Offset

1,3

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 Corollary 2.4 p. 5.

Example

Initial rows are:
    1,
   -1,    8,    -1,
    4,  -76,   264,   -76,     4,
  -33, 1248, -9735, 22080, -9735, 1248, -33,
  ...

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[(2 k - 1)! G[k, m], {k, 1, 6}, {m, 1, 2 k - 1}] // Flatten (* Jean-François Alcover, Sep 06 2018 *)

Crossrefs

Cf. A280036, A280037.

Sequence in context: A298523 A223710 A163898 * A202284 A231772 A338935

Adjacent sequences: A280037 A280038 A280039 * A280041 A280042 A280043

Keyword

sign,tabf

Author

N. J. A. Sloane, Dec 28 2016

Extensions

a(17) and beyond from Lars Blomberg, Jul 07 2017

Status

approved