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%I #13 Jun 18 2024 11:09:14
%S 1,14,115,640,3049,13494,57491,239768,986976,4027666,16335660,
%T 65955960,265386251,1064993622,4264898875,17051078256,68080259516,
%U 271537515786,1082098938452,4309269809044,17151303222746,68232856509950,271350536990740,1078796298028680,4287906741748940
%N a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026615.
%H G. C. Greubel, <a href="/A026959/b026959.txt">Table of n, a(n) for n = 3..1000</a>
%F a(n) = binomial(2*n, n+3)*(49*n^4 - 154*n^3 + 279*n^2 - 390*n + 288)/(4! * binomial(2*n, 4)) - (1/3)*(n-2)*(2*n^2 - 5*n + 9) + [n=3]. - _G. C. Greubel_, Jun 17 2024
%t Table[(2*n-4)!*(49*n^4 -154*n^3 +279*n^2 -390*n +288)/((n-3)!*(n+3)!) - (n-2)*(2*n^2-5*n+9)/3 +Boole[n==3], {n,3,40}] (* _G. C. Greubel_, Jun 17 2024 *)
%o (Magma) [n eq 3 select 1 else Binomial(2*n,n+3)*(49*n^4 -154*n^3 +279*n^2 -390*n +288)/(24* Binomial(2*n,4)) -(n-2)*(2*n^2-5*n+9)/3: n in [3..40]]; // _G. C. Greubel_, Jun 17 2024
%o (SageMath) [binomial(2*n,n+3)*(49*n^4 -154*n^3 +279*n^2 -390*n +288)/(24*binomial(2*n,4)) -(1/3)*(n-2)*(2*n^2-5*n+9) +int(n==3) for n in range(3,41)] # _G. C. Greubel_, Jun 17 2024
%Y Cf. A026615, A026616, A026617, A026618, A026619, A026620, A026621.
%Y Cf. A026622, A026623, A026624, A026625, A026956, A026957, A026958.
%Y Cf. A026960.
%K nonn
%O 3,2
%A _Clark Kimberling_
%E More terms from _Sean A. Irvine_, Oct 20 2019
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