A349073 a(n) = U(2*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.

1, 3, 209, 40391, 15003009, 9127651499, 8254109243953, 10393834843080975, 17391182043967249409, 37326390852372133364819, 99976027392046047055178001, 326887883645157139828711692503, 1281398359905415379814555044995201, 5932135472283024519893762690145006075

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..193

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

Wikipedia, Chebyshev polynomials.

Formula

For n>1, a(n) = ((n + sqrt(n^2-1))^(2*n+1) - (n - sqrt(n^2-1))^(2*n+1)) / (2*sqrt(n^2-1)).

a(n) ~ 2^(2*n) * n^(2*n).

Mathematica

Table[ChebyshevU[2*n, n], {n, 0, 15}]

Prog

(PARI) a(n) = polchebyshev(2*n, 2, n); \\ Michel Marcus, Nov 07 2021
(Python)
from sympy import chebyshevu
def A349073(n): return chebyshevu(n<<1, n) # Chai Wah Wu, Nov 08 2023

Crossrefs

Cf. A173129, A323118, A349071, A349074, A349075.

Sequence in context: A212997 A157390 A251864 * A063407 A303214 A258110

Adjacent sequences: A349070 A349071 A349072 * A349074 A349075 A349076

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved