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..800
FORMULA
G.f.: (1+3*sqrt(1-16*x))/(4*sqrt(1-16*x)).
n*a(n) +8*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Nov 24 2012
E.g.f.: (3 + exp(8*x) * BesselI(0,8*x)) / 4. - Ilya Gutkovskiy, Nov 17 2021
MATHEMATICA
Join[{1}, Table[4^(n-1)*Binomial[2*n, n], {n, 1, 30}]] (* G. C. Greubel, Dec 31 2017 *)
PROG
(Magma) [(3*0^n + 4^n*Binomial(2*n, n))/4: n in [ 0..20]]; // Vincenzo Librandi, Nov 24 2012
(PARI) for(n=0, 30, print1((3*0^n + 4^n*binomial(2*n, n))/4, ", ")) \\ G. C. Greubel, Dec 31 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 24 2004
STATUS
approved