A177166 - OEIS

%I #7 Oct 08 2016 09:14:03

%S 1,9,17,114,533,3406,20281,132987,868359,5880694,40168271,279254657,

%T 1959385953,13894772276,99289815837,714761301180,5176706895201,

%U 37701431645548,275906664244201,2028001454003211,14964925167434231

%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)=9, k=0 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=0, l=-1).

%F Conjecture: (n+1)*a(n) +2(1-3n)*a(n-1) +(51-23n)*a(n-2) +4*(16n-49)*a(n-3) +36*(4-n)*a(n-4)=0. - _R. J. Mathar_, Nov 27 2011

%e a(2)=2*1*9-1=17. a(3)=2*1*17+81-1=114.

%p l:=-1: : k := 0 : m:=9: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. A177165.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 04 2010