%I #27 Jan 08 2019 05:18:08

%S 1,14,1155,238204,92208005,57723886506,53303126198791,

%T 68201766898127864,115562692712642803209,250568062566458497345990,

%U 676789415690723540731574411,2228525638897473760683321942900,8788368165086865758098175776802701,40895852668226096118083495224349942114

%N a(n) = U_{2*n-1}(n)/(2*n) where U_{n}(x) is a Chebyshev polynomial of the second kind.

%H Seiichi Manyama, <a href="/A323181/b323181.txt">Table of n, a(n) for n = 1..194</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.

%F a(n) = U_{n-1}(2*n^2-1).

%F a(n) = (1/2) * Sum_{k=0..n-1} binomial(2*n,2*k+1)*(n^2-1)^(n-1-k)*n^(2*k).

%F a(n) ~ 2^(2*n - 2) * n^(2*n - 2). - _Vaclav Kotesovec_, Jan 07 2019

%t Table[ChebyshevU[2*n - 1, n]/(2*n), {n, 1, 15}] (* _Vaclav Kotesovec_, Jan 07 2019 *)

%o (PARI) {a(n) = polchebyshev(2*n-1, 2, n)/(2*n)}

%o (PARI) {a(n) = polchebyshev(n-1, 2, 2*n^2-1)}

%o (PARI) {a(n) = sum(k=0, n-1, binomial(2*n, 2*k+1)*(n^2-1)^(n-1-k)*n^(2*k))/2}

%Y Cf. A056220, A173194.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 06 2019