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A176759 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=0, k=1 and l=-1.

%I A176759 #6 Feb 18 2016 14:32:07
%S A176759 1,0,1,4,11,27,67,178,505,1489,4473,13593,41749,129579,406021,1282464,
%T A176759 4077987,13041655,41919347,135352451,438827223,1427986281,4662359911,
%U A176759 15268900019,50143755435,165095296125,544847069819,1802020334105
%N A176759 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=0, k=1 and l=-1.
%F A176759 G.f f: f(z)=(1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=1, l=-1).
%F A176759 Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +(-29*n+82)*a(n-3) +4*(5*n-19)*a(n-4) +4*(-n+5)*a(n-5)=0. - _R. J. Mathar_, Feb 18 2016
%e A176759 a(2)=2*1*0+2-1=1. a(3)=2*1*1+2+0^2+1-1=4. a(4)=2*1*4+2+2*0*1+2-1=11.
%p A176759 l:=-1: : k := 1 : m:=0:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
%p A176759 taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);
%Y A176759 Cf. A176757.
%K A176759 easy,nonn
%O A176759 0,4
%A A176759 _Richard Choulet_, Apr 25 2010