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A349073
a(n) = U(2*n, n), where U(n, x) is the Chebyshev polynomial of the second kind.
6
1, 3, 209, 40391, 15003009, 9127651499, 8254109243953, 10393834843080975, 17391182043967249409, 37326390852372133364819, 99976027392046047055178001, 326887883645157139828711692503, 1281398359905415379814555044995201, 5932135472283024519893762690145006075
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the Second Kind.
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 07 2021
STATUS
approved