Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Oct 22 2023 11:36:30
%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