A177185 - OEIS

%I #5 Feb 21 2016 15:54:56

%S 1,10,17,130,595,4073,24459,167500,1117353,7829307,54906873,393635415,

%T 2840684509,20748878557,152583436237,1130904562550,8430522519235,

%U 63205880187653,476121899816163,3602456244620557,27363055273700095

%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)=10, k=-1 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=-1, l=-1).

%F Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +3*(-7*n+17)*a(n-2) +(107*n-334)*a(n-3) +4*(-31*n+125)*a(n-4) +44*(n-5)*a(n-5)=0. - _R. J. Mathar_, Feb 21 2016

%e a(2)=2*1*10-2-1=17. a(3)=2*1*17-2+100-1-1=130.

%p l:=-1: : k := -1 : for m from 0 to 10 do 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): od;

%Y Cf. A177184.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 04 2010