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