A334088 a(n) = sqrt(Resultant(T(2*n,x/2), T(2*n,i*x/2))), where T(n,x) is a Chebyshev polynomial of the first kind and i = sqrt(-1).

1, 1, 8, 676, 591872, 5347119376, 497996601804800, 477995151754478453824, 4727827717838439286122217472, 481856411624794348153802518369517824, 506033683217425527860454091268429289861152768

Offset: 0

Author

Seiichi Manyama, Apr 14 2020

Keywords

• nonn

Links

• Wikipedia, Chebyshev polynomials
• Wikipedia, Resultant

Crossrefs

Cf. A004003, A334089.

Programs

Mathematica

Table[Sqrt[Resultant[ChebyshevT[2*n, x/2], ChebyshevT[2*n, I*x/2], x]], {n, 0, 12}] (* Vaclav Kotesovec, Apr 14 2020 *)

PARI

{a(n) = sqrtint(polresultant(polchebyshev(2*n, 1, x/2), polchebyshev(2*n, 1, I*x/2)))}

Python

from math import isqrt
from sympy.abc import x
from sympy import resultant, chebyshevt, I
def A334088(n): return isqrt(resultant(chebyshevt(n<<1,x/2),chebyshevt(n<<1,I*x/2))) if n else 1 # Chai Wah Wu, Nov 07 2023

Formula

a(n) ~ exp(4*G*n^2/Pi) / 2^(2*n - 1/4), where G is Catalan's constant A006752. - Vaclav Kotesovec, Apr 14 2020