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 #27 Mar 05 2021 09:36:28
%S 1,0,1,26,577,15124,470449,17057046,708158977,33165873224,
%T 1730726404001,99612037019890,6269617090376641,428438743526336412,
%U 31592397706723526737,2500433598371461203374,211434761022028192051201,19023879409608991280267536
%N a(n) = T_{n}(n-1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
%H Seiichi Manyama, <a href="/A323117/b323117.txt">Table of n, a(n) for n = 0..351</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>.
%F a(n)^2 - ((n - 1)^2 - 1) * A323118(n-1)^2 = 1 for n > 0.
%F a(n) = A322836(n,n-1) for n > 0.
%F a(n) ~ exp(-1) * 2^(n-1) * n^n. - _Vaclav Kotesovec_, Jan 05 2019
%F a(n) = cos(n*arccos(n-1)). - _Seiichi Manyama_, Mar 05 2021
%F a(n) = n * Sum_{k=0..n} (2*n-4)^k * binomial(n+k,2*k)/(n+k) for n > 0. - _Seiichi Manyama_, Mar 05 2021
%t Table[ChebyshevT[n, n - 1], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 05 2019 *)
%o (PARI) a(n) = polchebyshev(n, 1, n-1);
%o (PARI) a(n) = round(cos(n*acos(n-1))); \\ _Seiichi Manyama_, Mar 05 2021
%o (PARI) a(n) = if(n==0, 1, n*sum(k=0, n, (2*n-4)^k*binomial(n+k, 2*k)/(n+k))); \\ _Seiichi Manyama_, Mar 05 2021
%Y Cf. A115066, A322836, A323118.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Jan 05 2019