A240582 Largest absolute value of coefficient in the expression for the discriminant of a generic polynomial of degree n.

1, 4, 27, 256, 3750, 77760, 1728720, 55494528, 1948916016, 146502720000, 9131329626090

Offset

1,2

References

B. L. van der Waerden, Modern Algebra, Ungar, NY, Vol. I, 1953, pp. 82-83.

Links

Table of n, a(n) for n=1..11.

Example

For n=3, f(x) = a x^3 + b x^2 + c x + d, discriminant = b^2 c^2 - 4 a c^3 - 4 b^3 d + 18 a b c d - 27 a^2 d^2. The largest absolute value of a coefficient is 27.

Maple

f := proc(n) local x, a, i; maxnorm(discrim(add(a[i]*x^i, i=0..n), x)) end: # Roman Pearce, Aug 29 2014

Mathematica

n = 6;
Table[List @@ Discriminant[Sum[a[j] x^j, {j, 0, i}], x] /. a[_] -> 1 //
    Abs // Max, {i, n}]

Crossrefs

Sequence in context: A301742 A050764 A302108 * A338693 A360776 A360728

Adjacent sequences: A240579 A240580 A240581 * A240583 A240584 A240585

Keyword

nonn,more

Author

Albert Lau, Apr 08 2014

Extensions

a(9)-a(11) from Roman Pearce, Aug 29 2014

Status

approved