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
Keywords
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.
Programs
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Mathematica
Table[ChebyshevU[n, 2*n], {n, 0, 20}] -
PARI
a(n) = polchebyshev(n, 2, 2*n); \\ Michel Marcus, Nov 07 2021
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.