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A334124 a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{2*n}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).

%I A334124 #38 Nov 08 2023 01:48:48
%S A334124 1,3,71,17753,46069729,1234496016491,341133743251787719,
%T A334124 971684488369988888850993,28523907708086181923163934073729,
%U A334124 8628515016553040037389969912341438652243,26895841132028233579514694272575933932911355677831
%N A334124 a(n) = 2^n * sqrt(Resultant(U_{2*n}(x/2), T_{2*n}(i*x/2))), where T_n(x) is a Chebyshev polynomial of the first kind, U_n(x) is a Chebyshev polynomial of the second kind and i = sqrt(-1).
%H A334124 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>
%H A334124 Wikipedia, <a href="https://en.wikipedia.org/wiki/Resultant">Resultant</a>
%F A334124 a(n) = A103997(n,n).
%F A334124 a(n) ~ 2^(1/4) * exp(2*G*n*(2*n+1)/Pi) / (1 + sqrt(2))^n, where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Apr 16 2020, updated Jan 03 2021
%t A334124 Table[2^n * Sqrt[Resultant[ChebyshevU[2*n, x/2], ChebyshevT[2*n, I*x/2], x]], {n, 0, 12}] (* _Vaclav Kotesovec_, Apr 16 2020 *)
%o A334124 (PARI) {a(n) = sqrtint(4^n*polresultant(polchebyshev(2*n, 2, x/2), polchebyshev(2*n, 1, I*x/2)))}
%o A334124 (Python)
%o A334124 from math import isqrt
%o A334124 from sympy import resultant, chebyshevt, chebyshevu, I
%o A334124 from sympy.abc import x
%o A334124 def A334124(n): return isqrt(resultant(chebyshevu(n<<1,x/2),chebyshevt(n<<1,I*x/2))*(1<<(n<<1))) if n else 1 # _Chai Wah Wu_, Nov 07 2023
%Y A334124 Main diagonal of A103997.
%Y A334124 Cf. A004003, A334088.
%K A334124 nonn
%O A334124 0,2
%A A334124 _Seiichi Manyama_, Apr 15 2020