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 A037954 #13 Jun 21 2022 05:10:35
%S A037954 0,0,0,0,0,0,0,1,1,9,10,55,66,286,364,1365,1820,6188,8568,27132,38760,
%T A037954 116280,170544,490314,735471,2042975,3124550,8436285,13123110,
%U A037954 34597290,54627300,141120525,225792840
%N A037954 a(n) = binomial(n, floor((n-7)/2)).
%H A037954 G. C. Greubel, <a href="/A037954/b037954.txt">Table of n, a(n) for n = 0..1000</a>
%F A037954 (n+8)*(n-7)*a(n) = 2*(n)*a(n-1) + 4*(n-1)*n*a(n-2). - _R. J. Mathar_, Jul 26 2015
%F A037954 From _G. C. Greubel_, Jun 21 2022: (Start)
%F A037954 G.f.: ((1 +x -8*x^2 -7*x^3 +20*x^4 +14*x^5 -16*x^6 -7*x^7 +2*x^8) - (1 +x -6*x^2 - 5*x^3 +10*x^4 +6*x^5 -4*x^6 -x^7)*sqrt(1-4*x^2))/(2*x^8*sqrt(1-4*x^2)).
%F A037954 E.g.f.: BesselI(7, 2*x) + BesselI(8, 2*x). (End)
%t A037954 Table[Binomial[n,Floor[(n-7)/2]],{n,0,40}] (* _Harvey P. Dale_, Apr 15 2020 *)
%o A037954 (Magma) [Binomial(n, Floor((n-7)/2)): n in [0..40]]; // _G. C. Greubel_, Jun 21 2022
%o A037954 (SageMath) [binomial(n, (n-7)//2) for n in (0..40)] # _G. C. Greubel_, Jun 21 2022
%Y A037954 Cf. A035951, A035952, A035953, A035955, A035956, A035957.
%Y A037954 Cf. A089940, A101491.
%K A037954 nonn
%O A037954 0,10
%A A037954 _N. J. A. Sloane_