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%I #4 Mar 01 2016 16:24:23
%S 1,0,-3,-10,-25,-47,-41,160,1093,3987,10173,14835,-20271,-249343,
%T -1106383,-3335310,-6444345,-8187,67250223,363173857,1253557435,
%U 2927919099,2452549371,-18379498375,-127727251897,-501242196457
%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)=0, k=-1 and l=-1.
%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=-1, l=-1).
%F Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +13*(-n+2)*a(n-3) +4*(-n+5)*a(n-4) +4*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 01 2016
%e a(2)=2*1*0-2-1=-3. a(3)=2*1*(-3)-2+0^2-1-1=-10. a(4)=2*1*(-10)-2+2*0*(-3)-2-1=-25.
%p 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 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 easy,sign
%O 0,3
%A _Richard Choulet_, Apr 29 2010
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