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%I #6 Jan 20 2014 22:19:36
%S 1,1,0,-1,-4,-12,-34,-93,-248,-644,-1622,-3932,-9054,-19314,-36066,
%T -48953,8372,415848,2180870,8609676,29858358,95443242,286747530,
%U 815867808,2199049782,5577559986,13083598882,27240793594,44583397354
%N 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)=1, k=0 and l=-2.
%F 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 Conjecture: (n+1)*a(n) +2*(1-3*n)*a(n-1) +(9*n-13)*a(n-2) +2*(2*n-9)*a(n-3) +8*(4-n)*a(n-4)=0. - _R. J. Mathar_, Jul 24 2012
%e a(2)=2*1*1-2=0. a(3)=1-2=-1. a(4)=2*1*(-1)-2=-4.
%p l:=-2: : k := 0 : m:=1: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 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 Cf. A176752.
%K easy,sign
%O 0,5
%A _Richard Choulet_, Apr 25 2010
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