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%I #18 Oct 23 2023 12:55:16
%S 0,0,0,0,0,1,1,7,8,36,45,165,220,715,1001,3003,4368,12376,18564,50388,
%T 77520,203490,319770,817190,1307504,3268760,5311735,13037895,21474180,
%U 51895935,86493225,206253075
%N a(n) = binomial(n, floor((n-5)/2)).
%H G. C. Greubel, <a href="/A037953/b037953.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = binomial(n, A004526(n-5)). - _Wesley Ivan Hurt_, Nov 28 2013
%F (n+6)*(n-5)*a(n) = 2*(n)*a(n-1) + 4*(n-1)*n*a(n-2). - _R. J. Mathar_, Jul 26 2015
%F From _G. C. Greubel_, Jun 21 2022: (Start)
%F G.f.: ((1 +x -6*x^2 -5*x^3 +9*x^4 +5*x^5 -2*x^6) - (1 +x -4*x^2 -3*x^3 +3*x^4 +x^5)*sqrt(1-4*x^2))/(2*x^6*sqrt(1-4*x^2)).
%F E.g.f.: BesselI(5, 2*x) + BesselI(6, 2*x). (End)
%p A037953:=n->binomial(n, floor((n-5)/2)); seq(A037953(n), n=0..50); # _Wesley Ivan Hurt_, Nov 28 2013
%t Table[Binomial[n,Floor[(n-5)/2]],{n,0,40}] (* _Harvey P. Dale_, Oct 11 2012 *)
%o (Magma) [Binomial(n, Floor((n-5)/2)): n in [0..40]]; // _G. C. Greubel_, Jun 21 2022
%o (SageMath) [binomial(n, (n-5)//2) for n in (0..40)] # _G. C. Greubel_, Jun 21 2022
%o (PARI) a(n)=binomial(n,(n-5)\2) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y Cf. A035951, A035952, A035954, A035955, A035956, A035957.
%Y Cf. A004526, A089940, A101491.
%K nonn
%O 0,8
%A _N. J. A. Sloane_
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