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%I #5 Feb 21 2016 15:53:52
%S 1,10,18,134,626,4254,25850,177270,1192450,8392846,59270218,427294630,
%T 3103586514,22805459262,168767740698,1258575706582,9441189199010,
%U 71224314198510,539889535264490,4110514381564422,31418080601125746
%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)=10, 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*(-3*n+1)*a(n-1) +(-27*n+59)*a(n-2) +2*(38*n-117)*a(n-3) +44*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Feb 21 2016
%e a(2)=2*1*10-2=18. a(3)=2*1*18+100-2=134.
%p l:=-2: : k := 0 : for m from 0 to 10 do d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p),p=0..n)-2: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): od;
%Y Cf. A177171.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
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