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%I #5 Mar 02 2016 15:19:40
%S 1,4,7,28,109,487,2233,10666,52111,259957,1317331,6765121,35126623,
%T 184109599,972775495,5175914824,27709135453,149145574915,806659265809,
%U 4381711637563,23893807660885,130754073218149,717819706182061
%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)=4, 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) +3*(n+1)*a(n-2) +9*(3*n-10)*a(n-3) +36*(-n+4)*a(n-4) +12*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*4-2+1=7. a(3)=2*1*7-2+4^2-1+1=28. a(4)=2*1*28-2+2*4*7-2+1=109.
%p l:=1: : k := -1 : m:=4: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. A176964.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 29 2010
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