A176755 - OEIS

%I #5 Jan 20 2014 22:19:36

%S 1,3,4,15,52,208,846,3579,15456,68096,304570,1379980,6319978,29211278,

%T 136086710,638364319,3012609980,14293438828,68139158918,326218902372,

%U 1567802352910,7561126873098,36581288824402,177496766695528

%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)=3, k=0 and l=-2.

%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=0, l=-2).

%F 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 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 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 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. A176654.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, Apr 25 2010