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%I #5 Mar 02 2016 15:48:25
%S 1,7,11,67,283,1619,8667,50707,296283,1790163,10921563,67745043,
%T 424241371,2684071891,17112955099,109899184403,710063310427,
%U 4612990492883,30113345315163,197433924622099,1299499526756827
%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)=7, 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) +9*(-n+3)*a(n-2) +(71*n-226)*a(n-3) +4*(-22*n+89)*a(n-4) +32*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*7-2-1=11. a(3)=2*1*11-2+49-1-1=67.
%p l:=-1: : k := -1 : m:=7: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. A177181.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
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