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A349072 a(n) = T(n, 3*n), where T(n, x) is the Chebyshev polynomial of the first kind.

%I A349072 #22 Nov 09 2023 08:54:40
%S A349072 1,3,71,2889,164737,12082575,1083358151,114812765781,14040770918401,
%T A349072 1946133989077851,301491888156044999,51624542295308885793,
%U A349072 9681761035138427706241,1973656779656041723763559,434528364117341972641648967,102755067271708508826774929325
%N A349072 a(n) = T(n, 3*n), where T(n, x) is the Chebyshev polynomial of the first kind.
%C A349072 In general, for k>=1, T(n, k*n) ~ 2^(n-1) * k^n * n^n.
%H A349072 Seiichi Manyama, <a href="/A349072/b349072.txt">Table of n, a(n) for n = 0..306</a>
%H A349072 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html">Chebyshev Polynomial of the First Kind</a>.
%H A349072 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F A349072 a(n) = cosh(n*arccosh(3*n)).
%F A349072 a(n) = ((3*n + sqrt(9*n^2-1))^n + (3*n - sqrt(9*n^2-1))^n)/2.
%F A349072 a(n) ~ 2^(n-1) * 3^n * n^n.
%t A349072 Table[ChebyshevT[n, 3*n], {n, 0, 20}]
%o A349072 (PARI) a(n) = polchebyshev(n, 1, 3*n); \\ _Michel Marcus_, Nov 07 2021
%o A349072 (Python)
%o A349072 from sympy import chebyshevt
%o A349072 def A349072(n): return chebyshevt(n,3*n) # _Chai Wah Wu_, Nov 08 2023
%Y A349072 Cf. A053120, A115066, A349070, A349071, A349076.
%K A349072 nonn
%O A349072 0,2
%A A349072 _Vaclav Kotesovec_, Nov 07 2021