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A340295 a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - sin(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).

%I A340295 #20 Jan 04 2021 04:49:04
%S A340295 1,13,18281,2732887529,43384923739812577,73125714588602035608260981,
%T A340295 13085551252412040683513520733767180041,
%U A340295 248596840858215958581954513797323868183183928594833
%N A340295 a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - sin(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).
%C A340295 a(n)/A001570(n+1) is an integer.
%H A340295 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>
%H A340295 Wikipedia, <a href="https://en.wikipedia.org/wiki/Resultant">Resultant</a>
%F A340295 a(n) = A334089(2*n+1).
%F A340295 a(n) ~ exp(2*G*(2*n+1)^2/Pi) / 2^(3*n + 7/8), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Jan 04 2021
%t A340295 Table[Resultant[ChebyshevT[4*n+2, x/2], ChebyshevT[4*n+2, I*x/2], x]^(1/4) / 2^n, {n, 0, 10}] (* _Vaclav Kotesovec_, Jan 04 2021 *)
%o A340295 (PARI) default(realprecision, 120);
%o A340295 {a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(sin(j*Pi/(2*n+1))*cos(k*Pi/(2*n+1)))^2)))}
%o A340295 (PARI) {a(n) = sqrtint(sqrtint(polresultant(polchebyshev(4*n+2, 1, x/2), polchebyshev(4*n+2, 1, I*x/2))))/2^n}
%Y A340295 Cf. A001570, A334089, A340166, A340291, A340292.
%K A340295 nonn
%O A340295 0,2
%A A340295 _Seiichi Manyama_, Jan 03 2021