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%I #5 Mar 01 2016 16:20:20
%S 1,1,0,-2,-8,-25,-72,-197,-514,-1267,-2884,-5748,-8468,-119,68688,
%T 382434,1557232,5481369,17494220,51382510,138541696,335629309,
%U 685402744,919210879,-913800290,-13689355373,-71111254588,-287636394436
%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=-1 and l=0.
%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=0).
%F Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +3*(5*n-7)*a(n-2) +(-5*n+4)*a(n-3) +2*(-4*n+17)*a(n-4) +4*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 01 2016
%e a(2)=2*1*1-2=0. a(3)=2*1*0-2+1-1=-2. a(4)=2*1*(-2)-2+2*1*0-2=-8.
%p l:=0: : k := -1 : 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 : 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. A176854
%K easy,sign
%O 0,4
%A _Richard Choulet_, Apr 27 2010
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