A349071 a(n) = T(n, 2*n), where T(n, x) is the Chebyshev polynomial of the first kind.

1, 2, 31, 846, 32257, 1580050, 94558751, 6686381534, 545471324161, 50428155189474, 5210183616019999, 594949288292777902, 74404881332329766401, 10114032809617941274226, 1484781814660796486716447, 234114571438498509048719550, 39459584112457284328544403457

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..321

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

Wikipedia, Chebyshev polynomials.

Formula

a(n) = cosh(n*arccosh(2*n)).

a(n) = ((2*n + sqrt(4*n^2-1))^n + (2*n - sqrt(4*n^2-1))^n)/2.

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

Mathematica

Table[ChebyshevT[n, 2*n], {n, 0, 20}]

Prog

(PARI) a(n) = polchebyshev(n, 1, 2*n); \\ Michel Marcus, Nov 07 2021
(Python)
from sympy import chebyshevt
def A349071(n): return chebyshevt(n, n<<1) # Chai Wah Wu, Nov 08 2023

Crossrefs

Cf. A053120, A115066, A173129, A349072, A349073.

Sequence in context: A024235 A010789 A333349 * A224863 A263075 A217766

Adjacent sequences: A349068 A349069 A349070 * A349072 A349073 A349074

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved