OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = 4^n*Gamma(n+1/2)*(38 + 99*n + 49*n^2)*Pi^(-1/2)/Gamma(n+3) - 18 (based on guessed recurrence) - Mark van Hoeij, Oct 30 2011
From G. C. Greubel, Aug 22 2025: (Start)
a(n) = binomial(2*n, n) + 3*binomial(2*n+4, n+2) - 18.
G.f.: 2*(7 + 45*x + 2*x^2 - (5 - 23*x)*sqrt(1-4*x))/((1-x)*sqrt(1-4*x)*(1 + sqrt(1 - 4*x))^2).
E.g.f.: (1/x)*exp(2*x)*( 25*x*BesselI(0, 2*x) - 6*(1-4*x)*BesselI(1, 2*x) ) - 18*exp(x). (End)
MATHEMATICA
With[{b=Binomial}, Table[b[2*n, n] +3*b[2*n+4, n+2] -18, {n, 0, 40}]] (* G. C. Greubel, Aug 22 2025 *)
PROG
(Magma)
A026908:= func< n | (n+1)*Catalan(n) +3*(n+3)*Catalan(n+2) -18 >;
[A026908(n): n in [0..40]]; // G. C. Greubel, Aug 22 2025
(SageMath)
def A026908(n): return binomial(2*n, n) +3*binomial(2*n+4, n+2) -18
print([A026908(n) for n in range(41)]) # G. C. Greubel, Aug 22 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved
