This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A322899 #19 Apr 15 2020 05:27:07 %S A322899 1,7,577,119071,46099201,28860511751,26650854921601,34100354867927167, %T A322899 57780789062419261441,125283240358674708816199, %U A322899 338393251269110482793304001,1114259437504123772777608493087,4394174409561746573589926449440001 %N A322899 a(n) = T_{2*n}(n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind. %H A322899 Seiichi Manyama, <a href="/A322899/b322899.txt">Table of n, a(n) for n = 0..193</a> %H A322899 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>. %H A322899 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %F A322899 a(n) = T_{n}(2*n^2+4*n+1). %F A322899 a(n) = Sum_{k=0..n} binomial(2*n,2*k)*(n^2+2*n)^(n-k)*(n+1)^(2*k). %F A322899 a(n) ~ exp(2) * 2^(2*n-1) * n^(2*n). - _Vaclav Kotesovec_, Apr 15 2020 %t A322899 a[n_] := ChebyshevT[2n, n+1]; %t A322899 Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Jan 02 2019 *) %o A322899 (PARI) {a(n) = polchebyshev(2*n, 1, n+1)} %o A322899 (PARI) {a(n) = sum(k=0, n, binomial(2*n, 2*k)*(n^2+2*n)^(n-k)*(n+1)^(2*k))} %Y A322899 Diagonal of A188644. %K A322899 nonn %O A322899 0,2 %A A322899 _Seiichi Manyama_, Dec 30 2018