A191606 Let y=(1-sqrt(1-4*z))/(1+sqrt(1-4*z)) denote the g.f. for the Catalan numbers (A000108); sequence has g.f. sum(k>=1, y^(2^k)/(1+y^(2^(k+1))) ).

0, 0, 1, 4, 15, 56, 208, 768, 2823, 10352, 37944, 139232, 512048, 1888896, 6992960, 25989888, 96983687, 363368672, 1366820944, 5160846912, 19556183352, 74352602304, 283560228000, 1084470001024

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Ph. Flajolet and A. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math., vol 3 (1990) pp. 216-240.

Maple

y:=(1-sqrt(1-4*z))/(1+sqrt(1-4*z));
f:=add(y^(2^k)/(1+y^(2^(k+1))), k=1..12);
series(f, z, 24);

Mathematica

y[z_] = (1 - Sqrt[1 - 4*z])/(1 + Sqrt[1 - 4*z]);
f[z_] = Sum[y[z]^(2^k)/(1 + y[z]^(2^(k+1))), {k, 12}];
CoefficientList[Series[f[z], {z, 0, 23}], z]
(* Jean-François Alcover, Jun 30 2011, after Maple prog. *)

Crossrefs

Sequence in context: A077824 A291030 A217779 * A242495 A221859 A106707

Adjacent sequences: A191603 A191604 A191605 * A191607 A191608 A191609

Keyword

nonn

Author

N. J. A. Sloane, Jun 08 2011

Status

approved