OFFSET
0,2
COMMENTS
By the application of enumerating Rota-Baxter word (not following the g.f.) the value at index 0 is set to a(0)=1.
LINKS
Robert Israel, Table of n, a(n) for n = 0..1057
L. Guo, W. Y. Sit, Enumeration and generating functions of Rota-Baxter Words, Math. Comput. Sci. 4 (2010) 313-337, theorem 3.6 at z=2.
FORMULA
D-finite with recurrence (n+1)*a(n) +4*(-2*n+1)*a(n-1) +8*(-n+2)*a(n-2)=0. - R. J. Mathar, Jul 21 2017
MAPLE
f:= gfun:-rectoproc({8*n*a(n)+(12+8*n)*a(1+n)+(-3-n)*a(n+2), a(0) = 1, a(1) = 3}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Jul 21 2017
MATHEMATICA
CoefficientList[Series[(1-Sqrt[1-8x-8x^2])/(4x), {x, 0, 30}], x] (* Harvey P. Dale, Feb 10 2018 *)
PROG
(PARI) x='x+O('x^99); Vec((1-sqrt(1-8*x-8*x^2))/(4*x)) \\ Altug Alkan, Jul 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jul 21 2017
STATUS
approved