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A177180 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)=10, k=1 and l=-1.

%I A177180 #5 Jan 20 2014 22:19:36
%S A177180 1,10,21,144,711,4747,29767,205078,1409645,10043729,72216773,
%T A177180 528438373,3903255409,29138576719,219209569841,1661343858524,
%U A177180 12668020020047,97135000445375,748428139988567,5792032911677831,45000447097568843
%N A177180 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)=10, k=1 and l=-1.
%F A177180 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 A177180 Conjecture: (n+1)*a(n) +(2-7*n)*a(n-1) +3*(17-7*n)*a(n-2) +(91*n-278)*a(n-3) +4*(101-25*n)*a(n-4) +36*(n-5)*a(n-5)=0. - _R. J. Mathar_, Jul 24 2012
%p A177180 l:=-1: : k := 1 : for m from 0 to 10 do 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 A177180 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): od;
%Y A177180 Cf. A177179.
%K A177180 easy,nonn
%O A177180 0,2
%A A177180 _Richard Choulet_, May 04 2010