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 A370261 #15 Jul 24 2024 17:33:50
%S A370261 1,5,65,1449,46561,1968525,103565057,6531391313,480749649601,
%T A370261 40482981221781,3840053099665729,405275779792031225,
%U A370261 47113209228513626017,5982545638922153790749,823992221632687352744961,122360935410018418223907489,19489013519781051891806113153
%N A370261 a(n) = sqrt(A370259(2*n)/(n+1)) for n >= 1.
%C A370261 The sequence is conjectured to be integral.
%H A370261 Paolo Xausa, <a href="/A370261/b370261.txt">Table of n, a(n) for n = 1..300</a>
%F A370261 a(n) = sqrt( (T(2*n, 2*n+1) - 1)/((n+1)*(2*n)^3) ), where T(n, x) is the n-th Chebyshev polynomial of the first kind.
%p A370261 A370259 := n -> simplify( (ChebyshevT(n, n+1) - 1)/n^3 ):
%p A370261 seq(sqrt(A370259(2*n)/(n+1)), n = 1..20);
%t A370261 Table[Sqrt[(ChebyshevT[2*n, 2*n + 1] - 1)/(2*n)^3/(n + 1)], {n, 20}] (* _Paolo Xausa_, Jul 24 2024 *)
%o A370261 (Python)
%o A370261 from math import isqrt
%o A370261 from sympy import chebyshevt
%o A370261 def A370261(n): return isqrt((chebyshevt((m:=n<<1),m+1)-1)//((n+1)*m**3)) # _Chai Wah Wu_, Mar 13 2024
%Y A370261 Cf. A008310, A342205, A370259, A370260.
%K A370261 nonn,easy
%O A370261 1,2
%A A370261 _Peter Bala_, Mar 11 2024