|
%I #5 Mar 02 2016 16:00:15
%S 1,9,19,120,583,3688,22431,147801,979425,6696656,46323049,325632187,
%T 2312401207,16588994570,119955953891,873728090530,6403332744227,
%U 47188541743102,349446649937015,2599119078248913,19407853923218641
%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*(-3*n+1)*a(n-1) +(-23*n+51)*a(n-2) +56*(n-3)*a(n-3) +28*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*9+1=19. a(3)=2*1*19+81+1=120.
%p l:=1: : k := 0 : m :=9: d(0):=1:d(1):=m: for n from 1 to 28 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, 31); seq(d(n), n=0..29);
%Y Cf. A177129.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 03 2010
|
