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 A119975 #18 Sep 08 2022 08:45:25
%S A119975 1,2,7,22,77,266,947,3382,12217,44338,161855,593110,2181445,8046650,
%T A119975 29759147,110303798,409655281,1524056546,5678827511,21189499030,
%U A119975 79164147389,296094973418,1108623865123,4154794910518,15584520425641
%N A119975 E.g.f. exp(x)*(Bessel_I(0,2*sqrt(2)x) + Bessel_I(1,2*sqrt(2)x)/sqrt(2)).
%C A119975 Binomial transform of A098660. Binomial transform is A119976.
%C A119975 Hankel transform is A166232(n+1).
%H A119975 G. C. Greubel, <a href="/A119975/b119975.txt">Table of n, a(n) for n = 0..1000</a>
%F A119975 G.f.: 3/2*((1+3*x)/(6*x*sqrt(1-2*x-7*x^2))-1/(6*x)). - corrected by _Vaclav Kotesovec_, Jun 26 2013
%F A119975 a(n) = Sum_{k=0..n} C(n,k)*C(k,floor(k/2))2^floor(k/2);
%F A119975 a(n) = Sum_{k=0..n} Sum_{j=0..n} C(n,j-k)*C(k,j-k)*2^(j-k).
%F A119975 a(n) = (1/pi)*int(x^n*(x+3)/(4*sqrt(-x^2+2x+7)), x, 1-2*sqrt(2), 1+2*sqrt(2)).
%F A119975 a(n) = (1/pi)*int((x+1)^n*(x+4)/(4*sqrt(8-x^2)),x,-2*sqrt(2),2*sqrt(2)).
%F A119975 Conjecture: (n+1)*a(n) +(n-4)*a(n-1) +(9-13*n)*a(n-2) +21*(2-n)*a(n-3) =0. - _R. J. Mathar_, Dec 10 2011
%F A119975 a(n) ~ sqrt(16+11*sqrt(2))*(1+2*sqrt(2))^n/(4*sqrt(Pi*n)). - _Vaclav Kotesovec_, Jun 26 2013
%t A119975 Table[Sum[Binomial[n,k]*Binomial[k,Floor[k/2]]*2^Floor[k/2],{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o A119975 (PARI) x='x+O('x^50); Vec(3/2*((1+3*x)/(6*x*sqrt(1-2*x-7*x^2))-1/(6*x))) \\ _G. C. Greubel_, Mar 19 2017
%o A119975 (Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((3/2)*((1+3*x)/(6*x*Sqrt(1-2*x-7*x^2)) -1/(6*x)))); // _G. C. Greubel_, Aug 17 2018
%K A119975 easy,nonn
%O A119975 0,2
%A A119975 _Paul Barry_, Jun 02 2006