OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..351
Wikipedia, Chebyshev polynomials.
FORMULA
a(n)^2 - ((n - 1)^2 - 1) * A323118(n-1)^2 = 1 for n > 0.
a(n) = A322836(n,n-1) for n > 0.
a(n) ~ exp(-1) * 2^(n-1) * n^n. - Vaclav Kotesovec, Jan 05 2019
a(n) = cos(n*arccos(n-1)). - Seiichi Manyama, Mar 05 2021
a(n) = n * Sum_{k=0..n} (2*n-4)^k * binomial(n+k,2*k)/(n+k) for n > 0. - Seiichi Manyama, Mar 05 2021
MATHEMATICA
Table[ChebyshevT[n, n - 1], {n, 0, 20}] (* Vaclav Kotesovec, Jan 05 2019 *)
PROG
(PARI) a(n) = polchebyshev(n, 1, n-1);
(PARI) a(n) = round(cos(n*acos(n-1))); \\ Seiichi Manyama, Mar 05 2021
(PARI) a(n) = if(n==0, 1, n*sum(k=0, n, (2*n-4)^k*binomial(n+k, 2*k)/(n+k))); \\ Seiichi Manyama, Mar 05 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 05 2019
STATUS
approved