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-1) + 3*binomial(2*n+4, n+1) - 18.
G.f.: (3 - 9*x + 7*x^2 - 3*x^3 + 2*x^4 - (3 - 3*x + 7*x^2 + 17*x^3 + 12*x^4)*sqrt(1-4*x))/( 2*(1-x)*x^3*sqrt(1-4*x) ).
E.g.f.: 6 - 18*exp(x) - (1/x^2)*exp(2*x)*( 6*x(1-4*x)*BesselI(0, 2*x) - (6 - 12*x + 25*x^2)*BesselI(1, 2*x) ). (End)
a(n) ~ 49 * 4^n / sqrt(Pi*n). - Amiram Eldar, Oct 28 2025
MATHEMATICA
Table[n*CatalanNumber[n] +3*(n+2)*CatalanNumber[n+2] -18, {n, 40}] (* G. C. Greubel, Aug 22 2025 *)
PROG
(Magma)
A026910:= func< n | n*Catalan(n) +3*(n+2)*Catalan(n+2) -18 >;
[A026910(n): n in [1..40]]; // G. C. Greubel, Aug 22 2025
(SageMath)
def A026910(n): return binomial(2*n, n-1) +3*binomial(2*n+4, n+1) -18
print([A026910(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
