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%I #5 Mar 02 2016 15:17:49
%S 1,2,3,8,25,87,317,1190,4563,17797,70399,281813,1139659,4649403,
%T 19112963,79096156,329258425,1377798891,5792421109,24454224311,
%U 103631241913,440674939193,1879769835969,8041447249927,34490981798189
%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)=2, 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) +(11*n-13)*a(n-2) +3*(n-6)*a(n-3) +12*(-n+4)*a(n-4) +4*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*2-2+1=3. a(3)=2*1*3-2+2^2-1+1=8. a(4)=2*1*8-2+2*2*3-2+1=25.
%p l:=1: : k := -1 : m:=2: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. A176959.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 29 2010
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