%I #5 Mar 02 2016 15:16:01
%S 1,5,7,35,135,663,3159,16055,82423,434247,2317623,12547975,68644919,
%T 379136007,2110601527,11832031495,66734423095,378429810183,
%U 2156265145143,12339184691207,70884648719415,408640406413319
%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)=5, 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) +(-n+11)*a(n-2) +(47*n-154)*a(n-3) +4*(-16*n+65)*a(n-4) +24*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*5-2-1=7. a(3)=2*1*7-2+5^2-1-1=35. a(4)=2*1*35-2+2*5*7-2-1=135.
%p l:=-1: : k := -1 : m:=5: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. A176957.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 29 2010
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