A177170 - OEIS

%I #5 Jun 14 2016 12:38:56

%S 1,8,14,90,402,2438,13826,86014,533866,3431526,22262130,146919390,

%T 978782298,6589079958,44700139650,305468697294,2100216474090,

%U 14519814200198,100868678209298,703796972768062,4929877163487610

%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)=8, 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*(-3*n+1)*a(n-1) +(-19*n+43)*a(n-2) +6*(10*n-31)*a(n-3) +36*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Jun 14 2016

%e a(2)=2*1*8-2=14. a(3)=2*1*14+64-2=90.

%p l:=-2: : k := 0 : m:=8: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. A177169.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 04 2010