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 - 11*n + 6)*binomial(2*n, n)/(4*(n+1)*(2*n-1)) - [n=2].
G.f.: ( (2 - 7*x + 3*x^2) - (2 - 3*x + x^2 + 2*x^3)*sqrt(1-4*x) )/(2*x*sqrt(1-4*x)).
E.g.f.: (1/2)*exp(2*x)*( 3*(-1 + x)*BesselI(0, 2*x) + (4 - 3*x)*BesselI(1, 2*x) ) + (1/2)*(3 - x - x^2). (End)
MATHEMATICA
Table[(7*n^2-11*n+6)*Binomial[2*n, n]/(4*(n+1)*(2*n-1))-Boole[n==2], {n, 2, 40}] (* G. C. Greubel, Jun 13 2024 *)
PROG
(Magma) [n eq 2 select 1 else (7*n^2-11*n+6)*Catalan(n)/(4*(2*n-1)): n in [2..40]]; // G. C. Greubel, Jun 13 2024
(SageMath) [(7*n^2-11*n+6)*binomial(2*n, n)/(4*(n+1)*(2*n-1)) -int(n==2) for n in range(2, 41)] # G. C. Greubel, Jun 13 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved