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%I #5 Mar 02 2016 15:20:38
%S 1,5,9,41,169,825,4073,21113,111657,603961,3317353,18472697,104002729,
%T 591135417,3387188969,19545660025,113483969833,662493218361,
%U 3886235869033,22895917401593,135419375707561,803779534739897
%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)=5, 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) +(-n+11)*a(n-2) +3*(13*n-42)*a(n-3) +48*(-n+4)*a(n-4) +16*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016
%e a(2)=2*1*5-2+1=9. a(3)=2*1*9-2+5^2-1+1=41. a(4)=2*1*41-2+2*5*9-2+1=169.
%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. A176966.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 29 2010
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