A290147 Expansion of (1-sqrt(1-8*x-8*x^2))/(4*x).

1, 3, 12, 66, 408, 2712, 18912, 136488, 1010784, 7637664, 58650240, 456377664, 3590674176, 28516332288, 228297907200, 1840515987072, 14929020470784, 121749590032896, 997676696045568, 8210704762960896, 67835018440593408, 562407734010335232, 4677727530446635008

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

Cf. A025227.

Sequence in context: A082987 A086836 A074513 * A007871 A214565 A267323

Adjacent sequences: A290144 A290145 A290146 * A290148 A290149 A290150

Keyword

nonn

Author

R. J. Mathar, Jul 21 2017

Status

approved