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%I #18 Nov 08 2021 09:43:05
%S 1,6,143,5796,330049,24192090,2168392031,229755926568,28093745899009,
%T 3893604149949966,603151411514453999,103272803655639197580,
%U 19367259480582106560193,3947962681769909551857186,869179946261864224288867775,205535515565731164929726435280
%N a(n) = U(n, 3*n), where U(n, x) is the Chebyshev polynomial of the second kind.
%C In general, for k>=1, U(n, k*n) ~ 2^n * k^n * n^n.
%H Seiichi Manyama, <a href="/A349076/b349076.txt">Table of n, a(n) for n = 0..306</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html">Chebyshev Polynomial of the Second Kind</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F a(n) = ((3*n + sqrt(9*n^2-1))^(n+1) - (3*n - sqrt(9*n^2-1))^(n+1)) / (2*sqrt(9*n^2-1)).
%F a(n) ~ 6^n * n^n.
%t Table[ChebyshevU[n, 3*n], {n, 0, 20}]
%o (PARI) a(n) = polchebyshev(n, 2, 3*n); \\ _Michel Marcus_, Nov 07 2021
%Y Cf. A323118, A349071, A349072, A349074, A349075.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Nov 07 2021
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