OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..193
Wikipedia, Chebyshev polynomials.
FORMULA
For n > 0, a(n) = (1/n) * T_{2*n+1}(n) where T_{n}(x) is a Chebyshev polynomial of the first kind.
For n > 0, a(n) = (1/n) * cosh((2*n+1)*arccosh(n)).
a(n) ~ 4^n * n^(2*n). - Vaclav Kotesovec, Jan 03 2019
MATHEMATICA
a[0] = 1; a[n_] := 1/n ChebyshevT[2n+1, n];
Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Jan 02 2019 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(2*n+1, 2*k+1)*(n^2-1)^(n-k)*n^(2*k))}
(PARI) a(n) = if (n==0, 1, polchebyshev(2*n+1, 1, n)/n); \\ Michel Marcus, Jan 02 2019
(Magma) [&+[Binomial(2*n+1, 2*k+1)*(n^2-1)^(n-k)*n^(2*k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Jan 03 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 30 2018
STATUS
approved