%I #5 Mar 02 2016 15:30:59
%S 1,9,16,111,508,3268,19230,125859,815208,5494796,37280170,257711524,
%T 1796835778,12665947790,89949355454,643580501287,4632487753748,
%U 33531130466872,243877573413062,1781555056684620,13065400778105878
%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)=9, 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) +(-23*n+51)*a(n-2) +2*(34*n-105)*a(n-3) +40*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*9-2=16. a(3)=2*1*16+81-2=111.
%p l:=-2: : k := 0 : m:=9: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. A177170.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
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