|
%I #5 Mar 02 2016 15:31:49
%S 1,7,15,81,375,2113,11911,71221,433343,2704049,17125871,110044549,
%T 714925975,4690166833,31020995831,206646565637,1385159527343,
%U 9335979423089,63232378792703,430146956724677,2937659194003655
%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)=7, 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) +9*(-n+3)*a(n-2) +5*(11*n-34)*a(n-3) +4*(-16*n+65)*a(n-4) +24*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*7+2-1=15. a(3)=2*1*15+2+49+1-1=81.
%p l:=-1: : k := 1 : m:=5: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. A177176.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
|
