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A177168 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)=6, k=0 and l=-2.

%I A177168 #5 Jun 14 2016 12:42:09
%S A177168 1,6,10,54,226,1198,6186,34182,190962,1096286,6377338,37652278,
%T A177168 224654146,1353562766,8220739274,50284009702,309467901842,
%U A177168 1915015423678,11907759661850,74365628891286,466240095217378,2933473106737902
%N A177168 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)=6, k=0 and l=-2.
%F A177168 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=-2).
%F A177168 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-11*n+27)*a(n-2) +2*(22*n-69)*a(n-3) +28*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Jun 14 2016
%e A177168 a(2)=2*1*6-2=10. a(3)=2*1*10+36-2=54.
%p A177168 l:=-2: : k := 0 : m:=6: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 A177168 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 A177168 Cf. A176757.
%K A177168 easy,nonn
%O A177168 0,2
%A A177168 _Richard Choulet_, May 04 2010