OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..321
Wikipedia, Chebyshev polynomials.
FORMULA
a(n) = Sum_{k=0..n} binomial(2*n,2*k)*(n+1)^(n-k)*n^k. - Seiichi Manyama, Dec 26 2018
a(n) = T_{n}(2*n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind. - Seiichi Manyama, Dec 29 2018
MAPLE
A173174 := proc(n) cosh(2*n*arcsinh(sqrt(n))) ; expand(%) ; simplify(%) ; end proc: # R. J. Mathar, Feb 26 2011
MATHEMATICA
Table[Round[N[Cosh[(2 n) ArcSinh[Sqrt[n]]], 100]], {n, 0, 30}] (* Artur Jasinski *)
Join[{1}, a[n_]:=Sum[Binomial[2 n, 2 k] (n + 1)^(n - k) n^k, {k, 0, n}]; Array[a, 25]] (* Vincenzo Librandi, Dec 29 2018 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(2*n, 2*k)*(n+1)^(n-k)*n^k)} \\ Seiichi Manyama, Dec 26 2018
(PARI) {a(n) = polchebyshev(n, 1, 2*n+1)} \\ Seiichi Manyama, Dec 29 2018
(Magma) [&+[Binomial(2*n, 2*k)*(n+1)^(n-k)*n^k: k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Dec 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Feb 11 2010
EXTENSIONS
More terms from Seiichi Manyama, Dec 26 2018
STATUS
approved