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 A085458 #18 Mar 18 2023 08:49:14
%S A085458 1,4,20,116,708,4452,28532,185300,1215268,8030404,53381844,356577588,
%T A085458 2391430020,16092704292,108605848116,734783381652,4982063186916,
%U A085458 33844621986180,230306722637204,1569571734301172,10711405584991300
%N A085458 a(n) = 4*Sum_{i=0..n-1} C(2*i+1, i)*C(n-1, n-1-i)*(-1)^(n-1-i)*2^i for n > 0, a(0) = 1.
%H A085458 Vincenzo Librandi, <a href="/A085458/b085458.txt">Table of n, a(n) for n = 0..200</a>
%H A085458 Andrei Asinowski, Cyril Banderier and Benjamin Hackl, <a href="https://arxiv.org/abs/2003.04912">Flip-sort and combinatorial aspects of pop-stack sorting</a>, arXiv:2003.04912 [math.CO], 2020-2021; Discrete Mathematics & Theoretical Computer Science, April 30, 2021, vol. 22 no. 2. Formula 25.
%F A085458 G.f.: sqrt((1 + x)/(1 - 7*x)).
%F A085458 7^n = Sum_{i=0..n} Sum_{j=0..i} (-1)^(n-i)*a(j)*a(i-j).
%F A085458 Recurrence: n*a(n) = 2*(3*n-1)*a(n-1) + 7*(n-2)*a(n-2). - _Vaclav Kotesovec_, Oct 14 2012
%F A085458 a(n) ~ 2*sqrt(2)*7^(n-1/2)/sqrt(Pi*n). - _Vaclav Kotesovec_, Oct 14 2012
%t A085458 CoefficientList[Series[Sqrt[(1 + x)/(1 - 7x)], {x, 0, 25}], x]
%o A085458 (PARI) x='x+O('x^66); Vec(sqrt((1+x)/(1-7*x))) \\ _Joerg Arndt_, May 10 2013
%Y A085458 Cf. A085456 (signed version).
%K A085458 easy,nonn
%O A085458 0,2
%A A085458 Mario Catalani (mario.catalani(AT)unito.it), Jul 02 2003