%I #12 Sep 08 2022 08:44:49

%S 1,22,155,709,2587,8273,24416,68595,187030,500950,1327986,3499982,

%T 9195035,24115804,63192397,165512723,433410661,1134800215,2971089810,

%U 7778591025,20364830496,53316076892,139583609940,365435000524,956721681957,2504730383698,6557469861231

%N a(n) = T(2*n+1, n+3), T given by A027935.

%H G. C. Greubel, <a href="/A027943/b027943.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-26,45,-45,26,-8,1).

%F G.f.: x^2*(1+14*x+5*x^2-4*x^3) / ((1-x)^5*(1-3*x+x^2)). - _Colin Barker_, Feb 20 2016

%F From _G. C. Greubel_, Sep 28 2019: (Start)

%F a(n) = Sum_{j=0..n-2} binomial(2*n-j+1, 2*(n-j-2)).

%F a(n) = Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6. (End)

%p with(combinat); seq(fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6, n=2..40); # _G. C. Greubel_, Sep 28 2019

%t Table[Fibonacci[2*n+7] - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6, {n,2,40}]

%o (PARI) vector(30, n, my(m=n+1); fibonacci(2*m+7) - (4*m^4 +12*m^3 +35*m^2 +75*m +78)/6) \\ _G. C. Greubel_, Sep 28 2019

%o (Magma) [Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6: n in [2..40]]; // _G. C. Greubel_, Sep 28 2019

%o (Sage) [fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6 for n in (2..40)] # _G. C. Greubel_, Sep 28 2019

%o (GAP) List([2..40], n-> Fibonacci(2*n+7) - (78 +75*n +35*n^2 +12*n^3 +4*n^4)/6 ); # _G. C. Greubel_, Sep 28 2019

%Y Cf. A000045, A027935.

%K nonn

%O 2,2

%A _Clark Kimberling_

%E Terms a(22) onward added by _G. C. Greubel_, Sep 28 2019