A349075 a(n) = U(n, 2*n), where U(n, x) is the Chebyshev polynomial of the second kind.

1, 4, 63, 1704, 64769, 3168060, 189447551, 13389885712, 1092011153409, 100934312212404, 10426892198423999, 1190514147664125240, 148874434455514989313, 20235554722675691942764, 2970511463324707397138175, 468359315014627272862943520, 78938449723310515780367269889

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 Second Kind.

Wikipedia, Chebyshev polynomials.

Formula

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

a(n) ~ 4^n * n^n.

Mathematica

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

Prog

(PARI) a(n) = polchebyshev(n, 2, 2*n); \\ Michel Marcus, Nov 07 2021

Crossrefs

Cf. A323118, A349073, A349076.

Sequence in context: A227619 A177788 A293860 * A379660 A299428 A274392

Adjacent sequences: A349072 A349073 A349074 * A349076 A349077 A349078

Keyword

nonn

Author

Vaclav Kotesovec, Nov 07 2021

Status

approved