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%I #5 Mar 02 2016 15:32:46
%S 1,8,17,100,475,2843,16691,105026,668777,4379697,29069769,195897417,
%T 1334255973,9178287643,63648492949,444568586864,3124500279731,
%U 22080853944311,156808387564259,1118463885704019,8009066218515015
%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) +(67*n-206)*a(n-3) +4*(-19*n+77)*a(n-4) +28*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*8+2-1=17. a(3)=2*1*17+2+64+1-1=100.
%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);
%Y Cf. A177177.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010
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