OFFSET
0,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..386
Wikipedia, Chebyshev polynomials.
FORMULA
a(n) = 2 * cos(n*arccos((n+1)/2)).
a(n) = 2 * n * Sum_{k=0..n} (n-1)^k * binomial(n+k,2*k)/(n+k) for n > 0.
a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Apr 09 2021
Conjecture: a(p^r) == 1 (mod p^(2*r)) for positive integer r and all primes p >= 5. - Peter Bala, Mar 11 2024
MATHEMATICA
Table[2*ChebyshevT[n, (n+1)/2], {n, 0, 18}] (* Amiram Eldar, Apr 09 2021 *)
PROG
(PARI) a(n) = 2*polchebyshev(n, 1, (n+1)/2);
(PARI) a(n) = round(2*cos(n*acos((n+1)/2)));
(PARI) a(n) = if(n==0, 2, 2*n*sum(k=0, n, (n-1)^k*binomial(n+k, 2*k)/(n+k)));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 09 2021
STATUS
approved