A349076 - OEIS

%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