|
%I #17 Oct 23 2023 12:44:57
%S 0,0,0,0,0,0,1,1,8,9,45,55,220,286,1001,1365,4368,6188,18564,27132,
%T 77520,116280,319770,490314,1307504,2042975,5311735,8436285,21474180,
%U 34597290,86493225,141120525,347373600
%N a(n) = binomial(n, floor((n-6)/2)).
%H G. C. Greubel, <a href="/A037957/b037957.txt">Table of n, a(n) for n = 0..1000</a>
%F (n+7)*(n-6)*a(n) = 2*n*a(n-1) + 4*n*(n-1)*a(n-2). - _R. J. Mathar_, Jul 26 2015
%F From _G. C. Greubel_, Jun 20 2022: (Start)
%F G.f.: ((1 + x - 7*x^2 - 6*x^3 + 14*x^4 + 9*x^5 - 7*x^6 - 2*x^7) - (1 + x - 5*x^2 - 4*x^3 + 6*x^4 + 3*x^5 - x^6)*sqrt(1-4*x^2))/(2*x^7*sqrt(1-4*x^2)).
%F E.g.f.: BesselI(6, 2*x) + BesselI(7, 2*x). (End)
%t Table[Binomial[n,Floor[(n-6)/2]],{n,0,40}] (* _Harvey P. Dale_, May 16 2017 *)
%o (Magma) [Binomial(n, Floor((n-6)/2)): n in [0..40]]; // _G. C. Greubel_, Jun 20 2022
%o (SageMath) [binomial(n, (n-6)//2) for n in (0..40)] # _G. C. Greubel_, Jun 20 2022
%o (PARI) a(n)=binomial(n,n\2-3) \\ _Charles R Greathouse IV_, Oct 23 2023
%Y Cf. A035951, A035952, A035953, A035954, A035955, A035956.
%Y Cf. A089940, A101491.
%K nonn
%O 0,9
%A _N. J. A. Sloane_
|
