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%I #5 Mar 01 2016 16:21:13
%S 1,2,2,5,14,47,164,590,2156,7985,29900,113054,431132,1656641,6408776,
%T 24942227,97596698,383740409,1515431648,6008307998,23907184340,
%U 95439446687,382146649616,1534364232089,6176307411014,24919973908607
%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)=2, 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) +(11*n-13)*a(n-2) +(7*n-32)*a(n-3) +2*(-10*n+41)*a(n-4) +8*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 01 2016
%e a(2)=2*1*2-2=2. a(3)=2*1*2-2+2^2-1=5. a(4)=2*1*5-2+2*2*2-2=14.
%p l:=0: : k :=-1 : 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 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. A176855.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 27 2010
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