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 A188890 #29 Nov 08 2023 11:32:14
%S A188890 1,8,9216,1763704832,55786539933761536,291139753716719964894789632,
%T A188890 250571020614762113258116708732764160000,
%U A188890 35558299325468842404742419202148426327085023232000000,831952537599396321581603077837672266625608464198409017861335832068096
%N A188890 a(n) = 2^(n^2*2)*A004003(n).
%C A188890 The formula on line 3 of page 320 of the Levin et al. book has a typo: 2^(nm) should be 2^(mn/2). The main diagonal of the erroneous formula gives the present sequence.
%D A188890 Levin, David A.; Peres, Yuval; and Wilmer, Elizabeth L.; Markov Chains and Mixing Times, American Mathematical Society, Providence, RI, 2009.
%H A188890 Alois P. Heinz, <a href="/A188890/b188890.txt">Table of n, a(n) for n = 0..30</a>
%H A188890 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chebyshev_polynomials">Chebyshev polynomials</a>
%F A188890 a(n)^2 = Resultant(U(2*n,x), U(2*n,i*x)), where U(n,x) is a Chebyshev polynomial of the second kind and i = sqrt(-1). - _Seiichi Manyama_, Apr 14 2020
%F A188890 a(n) ~ 2^(2*n^2 + 1) * (sqrt(2)-1)^(2*n+1) * exp(G*(2*n+1)^2/Pi), where G is Catalan's constant A006752. - _Vaclav Kotesovec_, Apr 14 2020, updated Jan 03 2021
%p A188890 f:=(m,n)->
%p A188890 2^(m*n)*mul( mul(
%p A188890 (cos(Pi*i/(n+1))^2+cos(Pi*j/(m+1))^2), j=1..m/2), i=1..n/2);
%p A188890 g:=(m,n)->round(evalf(f(m,n),300));
%p A188890 t1:=[seq(g(2*n,2*n),n=0..10)];
%t A188890 Table[Sqrt[Resultant[ChebyshevU[2*n, x], ChebyshevU[2*n, I*x], x]], {n, 0, 10}] (* _Vaclav Kotesovec_, Apr 14 2020 *)
%o A188890 (PARI) {a(n) = sqrtint(polresultant(polchebyshev(2*n, 2, x), polchebyshev(2*n, 2, I*x)))} \\ _Seiichi Manyama_, Apr 14 2020
%o A188890 (Python)
%o A188890 from math import isqrt
%o A188890 from sympy import resultant, chebyshevu, I
%o A188890 from sympy.abc import x
%o A188890 def A188890(n): return isqrt(resultant(chebyshevu(n<<1,x),chebyshevu(n<<1,I*x))) if n else 1 # _Chai Wah Wu_, Nov 08 2023
%Y A188890 Cf. A004003.
%K A188890 nonn
%O A188890 0,2
%A A188890 _N. J. A. Sloane_, Apr 12 2011