login
A255587
Maximum absolute value of the coefficients of the n-th Swinnerton-Dyer polynomial.
2
1, 2, 10, 960, 13950764, 255690851718529024, 1771080720430629161685158978892152599456, 857834471403601877816627441633642526746656338035964968069692458744011458425706833248256
OFFSET
0,2
REFERENCES
Roman E. Maeder, Programming in Mathematica, Addison-Wesley, 1990, page 105.
EXAMPLE
SwinnertonDyerP(3, x) = x^8 - 40*x^6 + 352*x^4 - 960*x^2 + 576, hence a(3) = 960.
MAPLE
p:= proc(n) option remember; expand(`if`(n=0, x, mul(
subs(x=x+i*sqrt(ithprime(n)), p(n-1)), i=[1, -1])))
end:
a:= n-> max(map(abs, [coeffs(p(n))])):
seq(a(n), n=0..8); # Alois P. Heinz, Jun 12 2022
MATHEMATICA
SwinnertonDyerP[0, x_] := x; SwinnertonDyerP[n_, x_] := Module[{sd, srp = Sqrt[Prime[n]] }, sd[y_] = SwinnertonDyerP[n - 1, y]; Expand[sd[x + srp] sd[x - srp]]]; a[n_] := CoefficientList[SwinnertonDyerP[n, x], x^2] // Abs // Max; Table[a[n], {n, 1, 10}]
CROSSREFS
Sequence in context: A222420 A263921 A290495 * A137890 A074333 A008559
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jun 12 2022
STATUS
approved