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A349072
a(n) = T(n, 3*n), where T(n, x) is the Chebyshev polynomial of the first kind.
5
1, 3, 71, 2889, 164737, 12082575, 1083358151, 114812765781, 14040770918401, 1946133989077851, 301491888156044999, 51624542295308885793, 9681761035138427706241, 1973656779656041723763559, 434528364117341972641648967, 102755067271708508826774929325
OFFSET
0,2
COMMENTS
In general, for k>=1, T(n, k*n) ~ 2^(n-1) * k^n * n^n.
LINKS
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind.
FORMULA
a(n) = cosh(n*arccosh(3*n)).
a(n) = ((3*n + sqrt(9*n^2-1))^n + (3*n - sqrt(9*n^2-1))^n)/2.
a(n) ~ 2^(n-1) * 3^n * n^n.
MATHEMATICA
Table[ChebyshevT[n, 3*n], {n, 0, 20}]
PROG
(PARI) a(n) = polchebyshev(n, 1, 3*n); \\ Michel Marcus, Nov 07 2021
(Python)
from sympy import chebyshevt
def A349072(n): return chebyshevt(n, 3*n) # Chai Wah Wu, Nov 08 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 07 2021
STATUS
approved