OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
From G. C. Greubel, Aug 22 2025: (Start)
a(n) = (binomial(2*n, n) + 3*binomial(2*n+4, n+2) - 18)/2.
G.f.: 2*(3 + 25*x - x^2 - (3 - 13*x + x^2)*sqrt(1-4*x))/((1-x)*sqrt(1-4*x)*(1 + sqrt(1 - 4*x))^2).
E.g.f.: (1/(2*x))*exp(2*x)*( 25*x*BesselI(0, 2*x) - 6*(1-4*x)*BesselI(1, 2*x) ) - 9*exp(x) - 1/2. (End)
a(n) ~ 49 * 2^(2*n-1) / sqrt(Pi*n). - Amiram Eldar, Oct 28 2025
MATHEMATICA
With[{b=Binomial}, Table[(b[2*n, n] +3*b[2*n+4, n+2] -18)/2, {n, 40}]] (* G. C. Greubel, Aug 22 2025 *)
PROG
(Magma)
A026909:= func< n | ((n+1)*Catalan(n) +3*(n+3)*Catalan(n+2))/2 -9 >;
[A026909(n): n in [1..40]]; // G. C. Greubel, Aug 22 2025
(SageMath)
def A026909(n): return (binomial(2*n, n) +3*binomial(2*n+4, n+2))//2 -9
print([A026909(n) for n in range(1, 41)]) # G. C. Greubel, Aug 22 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms added by G. C. Greubel, Aug 22 2025
STATUS
approved
