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 A037951 #15 Jun 21 2022 17:10:44
%S A037951 0,0,0,1,1,5,6,21,28,84,120,330,495,1287,2002,5005,8008,19448,31824,
%T A037951 75582,125970,293930,497420,1144066,1961256,4457400,7726160,17383860,
%U A037951 30421755,67863915,119759850,265182525
%N A037951 a(n) = binomial(n, floor((n-3)/2)).
%H A037951 G. C. Greubel, <a href="/A037951/b037951.txt">Table of n, a(n) for n = 0..1000</a>
%F A037951 E.g.f.: Bessel_I(3, 2*x) + Bessel_I(4, 2*x) - _Paul Barry_, Feb 28 2006
%F A037951 (n+4)*(n-3)*a(n) = (-n^2+3*n+12)*a(n-1) + 2*(2*n+1)*(n-1)*a(n-2) + 4*(n-1)*(n-2)*a(n-3). - _R. J. Mathar_, Nov 24 2012
%F A037951 G.f.: ((1 +x -4*x^2 -3*x^3 +2*x^4) - (1 +x -2*x^2 -x^3)*sqrt(1-4*x^2))/(2*x^4*sqrt(1-4*x^2)). - _G. C. Greubel_, Jun 21 2022
%t A037951 Table[Binomial[n,Floor[(n-3)/2]],{n,0,40}] (* _Harvey P. Dale_, Jul 09 2017 *)
%o A037951 (Magma) [Binomial(n, Floor((n-3)/2)): n in [0..40]]; // _G. C. Greubel_, Jun 21 2022
%o A037951 (SageMath) [binomial(n, (n-3)//2) for n in (0..40)] # _G. C. Greubel_, Jun 21 2022
%Y A037951 Cf. A035952, A035953, A035954, A035955, A035956, A035957.
%Y A037951 Cf. A089940, A101491.
%K A037951 nonn
%O A037951 0,6
%A A037951 _N. J. A. Sloane_