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 A098521 #23 Sep 08 2022 08:45:15
%S A098521 0,0,1,3,14,50,195,721,2716,10116,37845,141295,528330,1975766,7395479,
%T A098521 27698685,103821240,389410568,1461605481,5489516955,20630539910,
%U A098521 77579118330,291893775019,1098848179561,4138773239892,15596070165900,58797332264125,221762856917511,836756771788098
%N A098521 E.g.f. exp(x)*BesselI(2,2*sqrt(2)*x)/2.
%C A098521 Binomial transform of e.g.f. BesselI(2,2*sqrt(2)*x)/2, or {0,0,1,0,8,0,60,0,448,0,3360,...} with g.f. ((1-4*x^2)-sqrt(1-8*x^2))/(8*x^2*sqrt(1-8*x^2)).
%H A098521 Vincenzo Librandi, <a href="/A098521/b098521.txt">Table of n, a(n) for n = 0..300</a>
%F A098521 G.f.: (1-2*x-3*x^2-(1-x)*sqrt(1-2*x-7*x^2))/(8*x^2*sqrt(1-2*x-7*x^2)).
%F A098521 a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(n-k, k+2)*2^k.
%F A098521 Conjecture: (n+2)*a(n) -(4n+3)*a(n-1) -3*(2n+1)*a(n-2) +(20n-29)*a(n-3) +21*(n-3)*a(n-4)=0. - _R. J. Mathar_, Dec 08 2011
%F A098521 Shorter recurrence (for n>=3): (n-2)*(n+2)*a(n) = n*(2*n-1)*a(n-1) + 7*(n-1)*n*a(n-2). - _Vaclav Kotesovec_, Dec 28 2012
%F A098521 a(n) ~ sqrt(8+2*sqrt(2))*(1+2*sqrt(2))^n/(8*sqrt(Pi*n)). - _Vaclav Kotesovec_, Dec 28 2012
%t A098521 CoefficientList[Series[(1-2*x-3*x^2-(1-x)*Sqrt[1-2*x-7*x^2]) / (8*x^2*Sqrt[1-2*x-7*x^2]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Dec 28 2012 *)
%o A098521 (PARI) x='x+O('x^66); concat([0,0],Vec((1-2*x-3*x^2-(1-x)*sqrt(1-2*x-7*x^2))/(8*x^2*sqrt(1-2*x-7*x^2)))) \\ _Joerg Arndt_, May 11 2013
%o A098521 (Magma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); [0,0] cat Coefficients(R!((1-2*x-3*x^2-(1-x)*Sqrt(1-2*x-7*x^2))/(8*x^2*Sqrt(1-2*x-7*x^2)))); // _G. C. Greubel_, Aug 17 2018
%Y A098521 Cf. A014531, A098518.
%K A098521 easy,nonn
%O A098521 0,4
%A A098521 _Paul Barry_, Sep 12 2004