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A176755 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=-2.

%I A176755 #5 Jan 20 2014 22:19:36
%S A176755 1,3,4,15,52,208,846,3579,15456,68096,304570,1379980,6319978,29211278,
%T A176755 136086710,638364319,3012609980,14293438828,68139158918,326218902372,
%U A176755 1567802352910,7561126873098,36581288824402,177496766695528
%N A176755 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=-2.
%F A176755 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=-2).
%F A176755 Conjecture: (n+1)*a(n) +2*(1-3*n)*a(n-1) +(n+3)*a(n-2) +2*(10*n-33)*a(n-3) +16*(4-n)*a(n-4) =0. - _R. J. Mathar_, Jul 24 2012
%e A176755 a(2)=2*1*3-2=4. a(3)=2*1*4+3^2-2=15. a(4)=2*1*15+2*3*4-2=52.
%p A176755 l:=-2: : 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 A176755 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 A176755 Cf. A176654.
%K A176755 easy,nonn
%O A176755 0,2
%A A176755 _Richard Choulet_, Apr 25 2010