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A026959
a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026615.
16
1, 14, 115, 640, 3049, 13494, 57491, 239768, 986976, 4027666, 16335660, 65955960, 265386251, 1064993622, 4264898875, 17051078256, 68080259516, 271537515786, 1082098938452, 4309269809044, 17151303222746, 68232856509950, 271350536990740, 1078796298028680, 4287906741748940
OFFSET
3,2
LINKS
FORMULA
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
MATHEMATICA
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 *)
PROG
(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
(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
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 20 2019
STATUS
approved