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A176752 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=0 and l=-2.

%I A176752 #4 Feb 18 2016 14:12:58
%S A176752 1,0,-2,-6,-14,-26,-30,30,330,1286,3538,6910,5434,-28618,-182302,
%T A176752 -654098,-1693750,-2852570,264050,25822302,126877786,411465750,
%U A176752 956711938,1191638734,-2480333334,-23263594746,-96124321390
%N A176752 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=0 and l=-2.
%F A176752 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=0, l=-2).
%F A176752 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(13*n-21)*a(n-2) +2*(-2*n+3)*a(n-3) +4*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Feb 18 2016
%e A176752 a(2)=0-2=-2. a(3)=2*1*(-2)-2=-6. a(4)=2*1*(-6)+0-2=-14.
%p A176752 l:=-2: : k := 0 : m:=2: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 A176752 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);
%K A176752 easy,sign
%O A176752 0,3
%A A176752 _Richard Choulet_, Apr 25 2010