OFFSET
0,2
COMMENTS
(1 + (k-1)*sqrt(1-4*k*x))/(k*sqrt(1-4*k*x)) is the g.f. for ((k-1)*0^n + k^n*binomial(2*n,n))/k.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..900
FORMULA
G.f.: 1/3 + 4*x/(sqrt(1-12*x)(1-sqrt(1-12*x))) = (1 + 2*sqrt(1-12*x))/(3*sqrt(1-12*x)).
n*a(n) +6*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 24 2012
E.g.f.: (2 + exp(6*x) * BesselI(0,6*x)) / 3. - Ilya Gutkovskiy, Nov 17 2021
MATHEMATICA
Join[{1}, Table[3^(n-1)*binomial(2*n, n), {n, 1, 30}]] (* G. C. Greubel, Dec 31 2017 *)
PROG
(Magma) [(2*0^n + 3^n*Binomial(2*n, n))/3: n in [ 0..20]]; // Vincenzo Librandi, Nov 24 2012
(PARI) for(n=0, 30, print1((2*0^n + 3^n*binomial(2*n, n))/3, ", ")) \\ G. C. Greubel, Dec 31 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 24 2004
STATUS
approved