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%I #5 Jan 20 2014 22:19:36
%S 1,10,23,150,765,5065,32337,223672,1556583,11178843,81228819,
%T 599868763,4475307567,33731219901,256268778463,1961208117130,
%U 15101975890677,116936866669157,909887821312929,7110983852617913,55793178281433653
%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=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*(n+1)*a(n) -n*(7*n-2)*a(n-1) -3*n*(7*n-17)*a(n-2) +n*(83*n-250)*a(n-3) -84*n*(n-4)*a(n-4) +28*n*(n-5)*a(n-5) =0. - _R. J. Mathar_, Jul 24 2012
%e a(2)=2*10+2+1=23. a(3)=2*1*23+2+10^2+1+1=150.
%p l:=1: : k := 1 : m :=10: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);
%Y Cf. A177125.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 03 2010
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