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 A322747 #21 Dec 29 2018 03:49:07 %S A322747 1,5,161,8749,665857,65160501,7793761249,1101696200669, %T A322747 179689877047297,33215554576822501,6862186181491284001, %U A322747 1566923219786361397005,391868347839681254572801,106523078497331434142611733,31273034455313887578671676257 %N A322747 a(n) = sqrt(1 + A322746(2*n)). %H A322747 Seiichi Manyama, <a href="/A322747/b322747.txt">Table of n, a(n) for n = 0..296</a> %H A322747 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>. %H A322747 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %F A322747 a(n) = Sum_{k=0..n} binomial(2*n, 2*k)*(2*n+1)^(n-k)*(2*n)^k. %F A322747 a(n) = A322790(2*n, n). %F A322747 a(n) = T_{n}(4*n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind. %F A322747 a(n) ~ exp(1/4) * 2^(3*n - 1) * n^n. - _Vaclav Kotesovec_, Dec 25 2018 %o A322747 (PARI) {a(n) = sum(k=0, n, binomial(2*n, 2*k)*(2*n+1)^(n-k)*(2*n)^k)} %o A322747 (PARI) {a(n) = polchebyshev(n, 1, 4*n+1)} %Y A322747 Cf. A322746, A322790. %K A322747 nonn %O A322747 0,2 %A A322747 _Seiichi Manyama_, Dec 25 2018