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 A343259 #21 Apr 11 2021 09:24:10 %S A343259 2,1,2,18,194,2525,39202,710647,14760962,345946302,9034502498, %T A343259 260219353691,8195978831042,280256592535933,10340256951198914, %U A343259 409468947059131650,17322711762013765634,779742677038695037937,37210469265847998489922,1876572071974094803391179 %N A343259 a(n) = 2 * T(n,n/2) where T(n,x) is a Chebyshev polynomial of the first kind. %H A343259 Seiichi Manyama, <a href="/A343259/b343259.txt">Table of n, a(n) for n = 0..386</a> %H A343259 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>. %F A343259 a(n) = 2 * cos(n*arccos(n/2)). %F A343259 a(n) = 2 * n * Sum_{k=0..n} (n-2)^k * binomial(n+k,2*k)/(n+k) for n > 0. %F A343259 a(n) ~ n^n. - _Vaclav Kotesovec_, Apr 09 2021 %t A343259 Table[2*ChebyshevT[n, n/2], {n, 1, 20}] (* _Amiram Eldar_, Apr 09 2021 *) %o A343259 (PARI) a(n) = 2*polchebyshev(n, 1, n/2); %o A343259 (PARI) a(n) = round(2*cos(n*acos(n/2))); %o A343259 (PARI) a(n) = if(n==0, 2, 2*n*sum(k=0, n, (n-2)^k*binomial(n+k, 2*k)/(n+k))); %Y A343259 Main diagonal of A298675. %Y A343259 Cf. A097690, A115066, A342205, A343260, A343261. %K A343259 nonn %O A343259 0,1 %A A343259 _Seiichi Manyama_, Apr 09 2021