|
%I #4 Mar 02 2016 15:49:31
%S 1,8,15,92,421,2535,14561,90770,568023,3668869,23962891,159056633,
%T 1066354423,7222075575,49299161087,338967663280,2344974625813,
%U 16312100074467,114021548709433,800494865098307,5641966696544221
%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=-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) +(-13*n+35)*a(n-2) +3*(25*n-78)*a(n-3) +84*(-n+4)*a(n-4) +28*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*8-2+1=15. a(3)=2*1*15-2+64-1+1=92.
%p l:=1: : k := -1 : 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);
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
|
