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 A258723 #20 Mar 11 2024 01:44:29
%S A258723 1,6,30,108,54,-3564,-41364,-314280,-1798362,-6972156,-1793340,
%T A258723 283697640,3341429820,25984971720,151750943640,596184213168,
%U A258723 101849014278,-25747257110940,-305001821608236,-2392882855430328,-14088646343199276,-55649498057805096,-7100681134947480
%N A258723 Expansion of 1/(1-12*x+48*x^2)^(1/2).
%H A258723 G. C. Greubel, <a href="/A258723/b258723.txt">Table of n, a(n) for n = 0..1000</a>
%H A258723 Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Szalay/szalay42.html">Diagonal Sums in the Pascal Pyramid, II: Applications</a>, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
%H A258723 Vaclav Kotesovec, <a href="/A258723/a258723.jpg">Graph - the asymptotic ratio</a>
%F A258723 G.f.: 1/(1-12*x+48*x^2)^(1/2).
%F A258723 E.g.f.: exp(6*x)*BesselJ(0,2*sqrt(3)*x).
%F A258723 If mod(n,6)=4 then a(n) ~ (-1)^((n+8)/6) * 3^((n+1)/2) * 4^(n-1) / (sqrt(Pi) * n^(3/2)), else a(n) ~ 3^(n/2) * 2^(2*n+1) * cos(Pi*(n-1)/6) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jun 08 2015
%F A258723 D-finite with recurrence n*a(n) +6*(-2*n+1)*a(n-1) +48*(n-1)*a(n-2)=0. [Belbachir]
%t A258723 CoefficientList[Series[1/(1-12*x+48*x^2)^(1/2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jun 08 2015 *)
%o A258723 (PARI) Vec(1/(1-12*x+48*x^2)^(1/2) + x^50) \\ _G. C. Greubel_, Feb 14 2017
%Y A258723 Cf. A144535, A144536, A240880.
%K A258723 sign
%O A258723 0,2
%A A258723 _Sergei N. Gladkovskii_, Jun 08 2015