A349070 - OEIS

%I #19 Nov 09 2021 05:25:34

%S 1,1,1351,3880899,28355806081,429364731169925,11731978174095849671,

%T 525735133485219615486151,36049049892983023583045990401,

%U 3588952618789973294871796462342089,497937643558017209960022199517744044999,93156956377055671178035977181412016527566091

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

%C In general, for k>=1, T(k*n, n) ~ 2^(k*n - 1) * n^(k*n).

%H Seiichi Manyama, <a href="/A349070/b349070.txt">Table of n, a(n) for n = 0..136</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html">Chebyshev Polynomial of the First Kind</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.

%F a(n) = cosh(3*n*arccosh(n)).

%F a(n) = ((n + sqrt(n^2-1))^(3*n) + (n - sqrt(n^2-1))^(3*n))/2.

%F a(n) ~ 2^(3*n-1) * n^(3*n).

%t Table[ChebyshevT[3*n, n], {n, 0, 13}]

%o (PARI) a(n) = polchebyshev(3*n, 1, n); \\ _Michel Marcus_, Nov 07 2021

%Y Cf. A053120, A115066, A173129, A349072, A349074.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Nov 07 2021