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A318192 a(n) = U_{n}(n)/(n+1) where U_{n}(x) is a Chebyshev polynomial of the second kind. 2

%I

%S 1,1,5,51,781,16005,411881,12776743,464278585,19350109449,

%T 910126036909,47694593157211,2755988277318277,174100457124362509,

%U 11937317942278298961,882942450221936166735,70077737629245663437041,5940877531422707027770385

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

%H Seiichi Manyama, <a href="/A318192/b318192.txt">Table of n, a(n) for n = 0..352</a>

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

%F a(n) = A323118(n)/(n+1).

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

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

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

%Y Cf. A323118.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 07 2019

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Last modified October 17 11:26 EDT 2019. Contains 328108 sequences. (Running on oeis4.)