OFFSET
0,4
EXAMPLE
Triangle begins:
n=0: 1;
n=1: -1, 1;
n=2: -3, -2, 1;
n=3: -16, -16, -2, 1;
n=4: 0, 100, -10, -10, 1;
n=5: -1296, 0, 324, -24, -13, 1;
n=6: 0, 0, 4116, 392, -175, -14, 1;
For example, the characteristic polynomial associated to M(7) is
q^7 - 12*q^6 - 352*q^5 - 512*q^4 + 12288*q^3 + 16384*q^2 - 131072*q + 0;
so the seventh row of the triangle is
0, -131072, 16384, 12288, -512, -352, -12, 1.
MAPLE
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(LinearAlgebra[
CharacteristicPolynomial](Matrix(n, (i, j)-> irem(i*j, n+1)), x)):
seq(T(n), n=0..10); # Alois P. Heinz, Mar 27 2022
MATHEMATICA
Table[(-1)^(p + 1)*CoefficientList[CharacteristicPolynomial[Table[Mod[k*Table[i, {i, 1, p - 1}], p], {k, 1, p - 1}], x], x], {p, 2, 20}]
PROG
(PARI) row(n) = Vecrev(charpoly(matrix(n, n, i, j, i*j%(n+1)))); \\ Kevin Ryde, Mar 27 2022
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Luca Onnis, Mar 27 2022
STATUS
approved