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%I #4 Mar 02 2016 15:16:56
%S 1,0,-1,-4,-11,-25,-47,-62,7,421,1883,5897,14599,27207,23759,-88160,
%T -611867,-2334109,-6792407,-15438797,-23262579,6709917,220802693,
%U 1059222003,3559089425,9375216161,18369306441,16084068633,-70367438799
%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) +3*(-7*n+18)*a(n-3) +12*(n-4)*a(n-4) +4*(-n+5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*0-2+1=-1. a(3)=2*1*(-1)-2+0-1+1=-4. a(4)=2*1*(-4)-2+2*0*(-1)-2+1=-11.
%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 0,4
%A _Richard Choulet_, Apr 29 2010
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