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A176749 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)=3, k=0 and l=-1.

%I A176749 #4 Feb 18 2016 14:16:22
%S A176749 1,3,5,18,65,262,1093,4731,20979,94930,436451,2033321,9577653,
%T A176749 45538184,218263593,1053456780,5115724797,24977183908,122537039845,
%U A176749 603755499411,2986339566083,14823218200440,73813096856015,368631268757920
%N A176749 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)=3, k=0 and l=-1.
%F A176749 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=0, l=-1).
%F A176749 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(n+3)*a(n-2) +4*(4*n-13)*a(n-3) +12*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Feb 18 2016
%e A176749 a(2)=2*1*3-1=5. a(3)=2*1*5+3^2-1=18. a(4)=2*1*18+2*3*5-1=65.
%p A176749 l:=-1: : k := 0 : m:=3: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 A176749 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 A176749 Cf. A176678.
%K A176749 easy,nonn
%O A176749 0,2
%A A176749 _Richard Choulet_, Apr 25 2010