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 A098522 #22 Feb 14 2024 07:48:51
%S A098522 0,0,1,3,18,70,330,1386,6160,26496,115965,502975,2194302,9553050,
%T A098522 41687737,181908195,794770200,3474159304,15199740171,66541189473,
%U A098522 291507681070,1277822445690,5604712643376,24596642511628,108001447419048,474459925386600,2085333645995275,9169506194833881
%N A098522 E.g.f. exp(x)*BesselI(2,2*sqrt(3)*x)/3.
%C A098522 Binomial transform of e.g.f. BesselI(2,2*sqrt(3)x)/3, or {0,0,1,0,12,0,135,0,1512,0,17010,...} with g.f. ((1-6x^2)-sqrt(1-12x^2))/(18x^2*sqrt(1-12x^2)).
%H A098522 Vincenzo Librandi, <a href="/A098522/b098522.txt">Table of n, a(n) for n = 0..300</a>
%F A098522 G.f.: (1-2*x-5*x^2-(1-x)*sqrt(1-2*x-11*x^2))/(18*x^2*sqrt(1-2*x-11*x^2)).
%F A098522 a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(n-k, k+2)*3^k.
%F A098522 D-finite with recurrence: (n-2)*(n+2)*a(n) - n*(2n-1)*a(n-1) - 11n*(n-1)*a(n-2) = 0. - _R. J. Mathar_, Dec 11 2011
%F A098522 a(n) ~ sqrt(18+3*sqrt(3))*(1+2*sqrt(3))^n/(18*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 15 2012
%t A098522 Table[SeriesCoefficient[(1-2*x-5*x^2-(1-x)*Sqrt[1-2*x-11*x^2])/(18*x^2*Sqrt[1-2*x-11*x^2]),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 15 2012 *)
%o A098522 (PARI) x='x+O('x^66); concat([0,0],Vec((1-2*x-5*x^2-(1-x)*sqrt(1-2*x-11*x^2))/(18*x^2*sqrt(1-2*x-11*x^2)))) \\ _Joerg Arndt_, May 12 2013
%Y A098522 Cf. A098519, A098521.
%K A098522 easy,nonn
%O A098522 0,4
%A A098522 _Paul Barry_, Sep 12 2004