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 A090004 #28 Jun 14 2022 08:32:57
%S A090004 1,4,32,320,3616,44160,568320,7587840,104042496,1455308800,
%T A090004 20671234048,297204973568,4315444576256,63173752913920,
%U A090004 931171553771520,13806071300751360,205737584679321600,3079516590086553600,46275305227975393280,697790255614687969280,10554814464110079508480
%N A090004 Expansion of L(x)^(1/2), where L(x) is the g.f. for the Catalan Larcombe-French sequence A053175.
%H A090004 Seiichi Manyama, <a href="/A090004/b090004.txt">Table of n, a(n) for n = 0..833</a>
%F A090004 a(n) = 2^n * A089603(n). - _Seiichi Manyama_, Jan 13 2019
%F A090004 a(n) ~ 2^(4*n - 1/2) / (n * sqrt(Pi*log(n))) * (1 - (gamma/2 + log(2))/log(n) + (3*gamma^2/8 + 3*log(2)*gamma/2 + 3*log(2)^2/2 - Pi^2/16) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Sep 29 2019
%t A090004 nmax = 25; CoefficientList[Series[(EllipticK[(8*x/(1 - 8*x))^2]/((1 - 8*x)*Pi/2))^(1/2), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 26 2019 *)
%o A090004 (PARI) Vec( 1/agm(1,1-16*x+O(x^66))^(1/2) ) \\ _Joerg Arndt_, Aug 14 2013
%Y A090004 Cf. A053175, A089602, A089603.
%K A090004 nonn,easy
%O A090004 0,2
%A A090004 _Peter J Larcombe_, Jan 19 2004
%E A090004 More terms from _Christian G. Bower_, Jan 19 2004