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A268482 Triangle that arise in the study of Galois polynomials. 0
1, -1, 8, 4, -76, 264, -33, 1248, -9735, 22080, 456, -32088, 440448, -2085096, 3715440, -9460, 1216600, -26297700, 205444800, -704121000, 1087450320, 274800, -64995600, 2073673920, -23974142160, 129203087760, -354403429920, 500558083200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..28.

Christian Günther, Kai-Uwe Schmidt, Lq norms of Fekete and related polynomials, arXiv:1602.01750 [math.NT], 2016.

EXAMPLE

First few rows are:

1;

-1, 8;

4, -76, 264;

-33, 1248, -9735, 22080;

456, -32088, 440448, -2085096, 3715440;

...

MATHEMATICA

c[k_] := c[k] = 1 - Sum[Binomial[k, j] Binomial[k-1, j-1] c[j], {j, k-1}];

eul[n_, x_] := Sum[(-1)^j Binomial[n+1, j] (x-j+1)^n, {j, 0, x+1}];

G[k_, m_] := G[k, m] = If [k==0 && m==0, 1, Sum[Binomial[k, j] Binomial[ k-1, j-1] c[j] Sum[eul[2j-1, i-1] G[k-j, m-i], {i, m}]/(2j-1)!, {j, k}]];

Table[(2n-1)! G[n, k], {n, 7}, {k, n}] // Flatten (* Jean-François Alcover, Sep 27 2018, from PARI *)

PROG

(PARI) C(k) = {my(j); 1 - sum(j=1, k-1, binomial(k, j)*binomial(k-1, j-1)*C(j))};

eul(n, x) = {my(j); sum(j=0, x+1, (-1)^j*binomial(n+1, j)*(x+1-j)^n)};

G(k, m) = if ((k==0) && (m==0), 1, sum(j=1, k, binomial(k, j)*binomial(k-1, j-1)*C(j)*sum(i=1, m, eul(2*j-1, i-1)*G(k-j, m-i))/(2*j-1)!));

tabl(nn) = for (n=1, nn, for (k=1, n, print1((2*n-1)!*G(n, k), ", ")); print(); );

CROSSREFS

Cf. A008292 (Eulerian numbers), A002190 (first column unsigned).

Sequence in context: A112583 A112589 A038282 * A231234 A096687 A326955

Adjacent sequences:  A268479 A268480 A268481 * A268483 A268484 A268485

KEYWORD

sign,tabl

AUTHOR

Michel Marcus, Feb 05 2016

STATUS

approved

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Last modified January 17 02:12 EST 2022. Contains 350377 sequences. (Running on oeis4.)