This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173194 #35 Jan 05 2019 13:21:45
%S A173194 0,0,9408,384199200,54471499791360,20405558846592060000,
%T A173194 16793517249722147195701440,26730228454204365035835498694848,
%U A173194 75019085697452515216001640927169855488,346154755746154620929434271983392498083891520
%N A173194 a(n) = -sin^2 (2*n*arccos n) = - sin^2 (2*n*arcsin n).
%H A173194 Seiichi Manyama, <a href="/A173194/b173194.txt">Table of n, a(n) for n = 0..107</a>
%H A173194 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F A173194 4*a(n) = ( (n+sqrt(n^2-1))^(2*n) - (n-sqrt(n^2-1))^(2*n) )^2. - _Artur Jasinski_, Feb 17 2010
%F A173194 From _Seiichi Manyama_, Jan 05 2019: (Start)
%F A173194 a(n) = (n^2-1) * n^2 * (Sum_{k=0..n-1} binomial(2*n,2*k+1)*(n^2-1)^(n-1-k)*n^(2*k))^2.
%F A173194 For n > 0, a(n) = (n^2-1) * U_{2*n-1}(n)^2 where U_{n}(x) is a Chebyshev polynomial of the second kind. (End)
%F A173194 a(n) ~ 2^(4*n - 2) * n^(4*n). - _Vaclav Kotesovec_, Jan 05 2019
%p A173194 A173194 := proc(n) ((n+sqrt(n^2-1))^(2*n)-(n-sqrt(n^2-1))^(2*n))^2 ; expand(%/4) ; simplify(%) ; end proc: # _R. J. Mathar_, Feb 26 2011
%t A173194 Round[Table[ -N[Sin[2 n ArcSin[n]], 100]^2, {n, 0, 15}]] (* _Artur Jasinski_ *)
%t A173194 Table[FullSimplify[(-1/2 (x - Sqrt[ -1 + x^2])^(2 x) + 1/2 (x + Sqrt[ -1 + x^2])^(2 x))^2], {x, 0, 7}] (* _Artur Jasinski_, Feb 17 2010 *)
%t A173194 Table[(n^2-1)*ChebyshevU[2*n-1, n]^2, {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 05 2019 *)
%o A173194 (PARI) {a(n) = (n^2-1)*n^2*(sum(k=0, n-1, binomial(2*n, 2*k+1)*(n^2-1)^(n-1-k)*n^(2*k)))^2} \\ _Seiichi Manyama_, Jan 05 2019
%o A173194 (PARI) {a(n) = (n^2-1)*polchebyshev(2*n-1, 2, n)^2} \\ _Seiichi Manyama_, Jan 05 2019
%Y A173194 Cf. A132592, A146311, A146312, A146313, A173115, A173116 A173121, A173127, A173128, A173129, A173130, A173131, A173133, A173134, A173148, A173151, A173170, A173171, A173174, A173175, A173176.
%K A173194 nonn
%O A173194 0,3
%A A173194 _Artur Jasinski_, Feb 12 2010
%E A173194 a(9) from _Seiichi Manyama_, Jan 05 2019