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%I #5 Mar 02 2016 15:14:48
%S 1,4,5,22,79,353,1551,7192,33789,162387,791013,3905115,19480249,
%T 98078377,497676217,2542770602,13070074447,67540608437,350682097767,
%U 1828571411257,9571449473587,50275314445747,264915701312467
%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)=4, 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+1)*a(n) +(-7*n+2)*a(n-1) +3*(n+1)*a(n-2) +(35*n-118)*a(n-3) +4*(-13*n+53)*a(n-4) +20*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*4-2-1=5. a(3)=2*1*5-2+4^4-1-1=22. a(4)=2*1*22-2+2*4*5-2-1=79.
%p l:=-1: : k := -1 : m:=4: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. A176956.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 29 2010
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