OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..193
Wikipedia, Chebyshev polynomials.
FORMULA
a(n) = Sum_{k=0..n} binomial(2*n+1,2*k)*(n^2+1)^(n-k)*n^(2*k).
a(n) ~ 2^(2*n) * n^(2*n). - Vaclav Kotesovec, Jan 02 2019
MATHEMATICA
Join[{1}, Table[Sum[Binomial[2 n + 1, 2 k] (n^2 + 1)^(n - k) n^(2 k), {k, 0, n}], {n, 20}]] (* Vincenzo Librandi, Jan 03 2019 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(2*n+1, 2*k)*(n^2+1)^(n-k)*n^(2*k))}
(Magma) [&+[Binomial(2*n+1, 2*k)*(n^2+1)^(n-k)*n^(2*k): k in [0..n]]: n in [0..15]]; // Vincenzo Librandi, Jan 03 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 02 2019
STATUS
approved