A191606 - OEIS

%I #18 Feb 06 2018 02:44:27

%S 0,0,1,4,15,56,208,768,2823,10352,37944,139232,512048,1888896,6992960,

%T 25989888,96983687,363368672,1366820944,5160846912,19556183352,

%U 74352602304,283560228000,1084470001024

%N 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))) ).

%H G. C. Greubel, <a href="/A191606/b191606.txt">Table of n, a(n) for n = 0..1000</a>

%H Ph. Flajolet and A. Odlyzko, <a href="http://algo.inria.fr/flajolet/Publications/FlOd90b.pdf">Singularity analysis of generating functions</a>, SIAM J. Discrete Math., vol 3 (1990) pp. 216-240.

%p y:=(1-sqrt(1-4*z))/(1+sqrt(1-4*z));

%p f:=add(y^(2^k)/(1+y^(2^(k+1))),k=1..12);

%p series(f,z,24);

%t y[z_] = (1 - Sqrt[1 - 4*z])/(1 + Sqrt[1 - 4*z]);

%t f[z_] = Sum[y[z]^(2^k)/(1 + y[z]^(2^(k+1))), {k, 12}];

%t CoefficientList[Series[f[z], {z, 0, 23}], z]

%t (* _Jean-François Alcover_, Jun 30 2011, after Maple prog. *)

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Jun 08 2011