cp's OEIS Frontend

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).

%I A334088 #20 Nov 08 2023 01:49:33
%S A334088 1,1,8,676,591872,5347119376,497996601804800,477995151754478453824,
%T A334088 4727827717838439286122217472,481856411624794348153802518369517824,
%U A334088 506033683217425527860454091268429289861152768
%N 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).
%H A334088 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>
%H A334088 Wikipedia, <a href="https://en.wikipedia.org/wiki/Resultant">Resultant</a>
%F A334088 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
%t A334088 Table[Sqrt[Resultant[ChebyshevT[2*n, x/2], ChebyshevT[2*n, I*x/2], x]], {n, 0, 12}] (* _Vaclav Kotesovec_, Apr 14 2020 *)
%o A334088 (PARI) {a(n) = sqrtint(polresultant(polchebyshev(2*n, 1, x/2), polchebyshev(2*n, 1, I*x/2)))}
%o A334088 (Python)
%o A334088 from math import isqrt
%o A334088 from sympy.abc import x
%o A334088 from sympy import resultant, chebyshevt, I
%o A334088 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
%Y A334088 Cf. A004003, A334089.
%K A334088 nonn
%O A334088 0,3
%A A334088 _Seiichi Manyama_, Apr 14 2020