|
%I #5 Mar 02 2016 15:33:37
%S 1,9,19,121,587,3717,22603,149065,988291,6762757,46812915,329336265,
%T 2340489211,16803807621,121604988955,886446236169,6501729726195,
%U 47952147336325,355387114288451,2645435985621257,19769671436457963
%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=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) +(-17*n+43)*a(n-2) +(79*n-242)*a(n-3) +4*(-22*n+89)*a(n-4) +32*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*9+2-1=19. a(3)=2*1*19+2+81+1-1=121.
%p l:=-1: : k := 1 : 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. A177178.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
|
