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A349073 a(n) = U(2*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.

%I A349073 #20 Feb 16 2025 08:34:02
%S A349073 1,3,209,40391,15003009,9127651499,8254109243953,10393834843080975,
%T A349073 17391182043967249409,37326390852372133364819,
%U A349073 99976027392046047055178001,326887883645157139828711692503,1281398359905415379814555044995201,5932135472283024519893762690145006075
%N A349073 a(n) = U(2*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.
%H A349073 Seiichi Manyama, <a href="/A349073/b349073.txt">Table of n, a(n) for n = 0..193</a>
%H A349073 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html">Chebyshev Polynomial of the Second Kind</a>.
%H A349073 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F A349073 For n>1, a(n) = ((n + sqrt(n^2-1))^(2*n+1) - (n - sqrt(n^2-1))^(2*n+1)) / (2*sqrt(n^2-1)).
%F A349073 a(n) ~ 2^(2*n) * n^(2*n).
%t A349073 Table[ChebyshevU[2*n, n], {n, 0, 15}]
%o A349073 (PARI) a(n) = polchebyshev(2*n, 2, n); \\ _Michel Marcus_, Nov 07 2021
%o A349073 (Python)
%o A349073 from sympy import chebyshevu
%o A349073 def A349073(n): return chebyshevu(n<<1,n) # _Chai Wah Wu_, Nov 08 2023
%Y A349073 Cf. A173129, A323118, A349071, A349074, A349075.
%K A349073 nonn
%O A349073 0,2
%A A349073 _Vaclav Kotesovec_, Nov 07 2021