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a(n) = binomial(n, floor((n-3)/2)).
5

%I #15 Jun 21 2022 17:10:44

%S 0,0,0,1,1,5,6,21,28,84,120,330,495,1287,2002,5005,8008,19448,31824,

%T 75582,125970,293930,497420,1144066,1961256,4457400,7726160,17383860,

%U 30421755,67863915,119759850,265182525

%N a(n) = binomial(n, floor((n-3)/2)).

%H G. C. Greubel, <a href="/A037951/b037951.txt">Table of n, a(n) for n = 0..1000</a>

%F E.g.f.: Bessel_I(3, 2*x) + Bessel_I(4, 2*x) - _Paul Barry_, Feb 28 2006

%F (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 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 Table[Binomial[n,Floor[(n-3)/2]],{n,0,40}] (* _Harvey P. Dale_, Jul 09 2017 *)

%o (Magma) [Binomial(n, Floor((n-3)/2)): n in [0..40]]; // _G. C. Greubel_, Jun 21 2022

%o (SageMath) [binomial(n, (n-3)//2) for n in (0..40)] # _G. C. Greubel_, Jun 21 2022

%Y Cf. A035952, A035953, A035954, A035955, A035956, A035957.

%Y Cf. A089940, A101491.

%K nonn

%O 0,6

%A _N. J. A. Sloane_