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

1, 3, 71, 2889, 164737, 12082575, 1083358151, 114812765781, 14040770918401, 1946133989077851, 301491888156044999, 51624542295308885793, 9681761035138427706241, 1973656779656041723763559, 434528364117341972641648967, 102755067271708508826774929325

Offset

0,2

Comments

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

Links

Seiichi Manyama, Table of n, a(n) for n = 0..306

Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind.

Wikipedia, Chebyshev polynomials.

Formula

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

a(n) = ((3*n + sqrt(9*n^2-1))^n + (3*n - sqrt(9*n^2-1))^n)/2.

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

Mathematica

Table[ChebyshevT[n, 3*n], {n, 0, 20}]

Prog

(PARI) a(n) = polchebyshev(n, 1, 3*n); \\ Michel Marcus, Nov 07 2021
(Python)
from sympy import chebyshevt
def A349072(n): return chebyshevt(n, 3*n) # Chai Wah Wu, Nov 08 2023

Crossrefs

Cf. A053120, A115066, A349070, A349071, A349076.

Sequence in context: A094458 A183548 A111649 * A272657 A226709 A226844

Adjacent sequences: A349069 A349070 A349071 * A349073 A349074 A349075

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved