OFFSET
3,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 3..1000
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
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Oct 20 2019
STATUS
approved