A349076 a(n) = U(n, 3*n), where U(n, x) is the Chebyshev polynomial of the second kind.

1, 6, 143, 5796, 330049, 24192090, 2168392031, 229755926568, 28093745899009, 3893604149949966, 603151411514453999, 103272803655639197580, 19367259480582106560193, 3947962681769909551857186, 869179946261864224288867775, 205535515565731164929726435280

Offset: 0

Author

Vaclav Kotesovec, Nov 07 2021

Keywords

• nonn

Comments

In general, for k>=1, U(n, k*n) ~ 2^n * 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 Second Kind.
• Wikipedia, Chebyshev polynomials.

Crossrefs

Cf. A323118, A349071, A349072, A349074, A349075.

Programs

Mathematica

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

PARI

a(n) = polchebyshev(n, 2, 3*n); \\ Michel Marcus, Nov 07 2021

Formula

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

a(n) ~ 6^n * n^n.