OFFSET
2,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
FORMULA
From G. C. Greubel, Jun 13 2024: (Start)
a(n) = (7*n^2 - 4*n + 4)*binomial(2*n, n-2)/(2*binomial(2*n, 2)) -[n=2].
G.f.: ( (2 - 9*x + 8*x^2 - 2*x^3) - (2 - 5*x + 2*x^2 + 2*x^4)*sqrt(1 - 4*x) )/(2*x^2*sqrt(1-4*x)).
E.g.f.: exp(2*x)*( (3 - x)*BesselI(0, 2*x) + (x - 1 - 2/x)*BesselI(1, 2*x) ) - (1 + x^2/2). (End)
MATHEMATICA
Table[(7*n^2-4*n+4)*Binomial[2*n, n-2]/(2*Binomial[2*n, 2]) -Boole[n==2], {n, 2, 40}] (* G. C. Greubel, Jun 13 2024 *)
PROG
(Magma) [n eq 2 select 1 else (7*n^2-4*n+4)*Binomial(2*n, n-2)/(2*Binomial(2*n, 2)): n in [2..40]]; // G. C. Greubel, Jun 13 2024
(SageMath) [(7*n^2-4*n+4)*binomial(2*n, n-2)/(2*binomial(2*n, 2)) - int(n==2) for n in range(2, 41)] # G. C. Greubel, Jun 13 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved