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%I #5 Mar 02 2016 15:58:12
%S 1,9,15,107,479,3103,18031,117727,755599,5064687,34093263,234114735,
%T 1620229839,11340760367,79951746767,567945479727,4058390653647,
%U 29163273207087,210568996777167,1527068200329007,11117641676731087
%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=-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) +(-17*n+43)*a(n-2) +(95*n-298)*a(n-3) +4*(-28*n+113)*a(n-4) +40*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*9-2-1=15. a(3)=2*1*15-2+81-1-1=107.
%p l:=-1: : k := -1 : 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. A177183.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
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