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

%I A318192 #21 Oct 22 2023 11:36:30
%S A318192 1,1,5,51,781,16005,411881,12776743,464278585,19350109449,
%T A318192 910126036909,47694593157211,2755988277318277,174100457124362509,
%U A318192 11937317942278298961,882942450221936166735,70077737629245663437041,5940877531422707027770385
%N A318192 a(n) = U_{n}(n)/(n+1) where U_{n}(x) is a Chebyshev polynomial of the second kind.
%H A318192 Seiichi Manyama, <a href="/A318192/b318192.txt">Table of n, a(n) for n = 0..352</a>
%H A318192 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F A318192 a(n) = A323118(n)/(n+1).
%F A318192 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 A318192 (PARI) {a(n) = polchebyshev(n, 2, n)/(n+1)}
%o A318192 (PARI) {a(n) = sum(k=0, n\2, binomial(n, 2*k)*(n^2-1)^k*n^(n-2*k)/(2*k+1))}
%Y A318192 Cf. A323118.
%K A318192 nonn
%O A318192 0,3
%A A318192 _Seiichi Manyama_, Jan 07 2019