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%I #5 Feb 29 2016 14:20:11
%S 1,2,7,22,77,297,1217,5192,22807,102427,468067,2169227,10170687,
%T 48155437,229916207,1105682842,5350944837,26040130117,127349649297,
%U 625556921097,3085016483557,15268791946687,75816909660597
%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)=2, k=1 and l=1.
%F Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +(-13*n+38)*a(n-3) +12*(n-4)*a(n-4) +4*(-n+5)*a(n-5)=0. - _R. J. Mathar_, Feb 29 2016
%e a(2)=2*1*2+2+1=7. a(3)=2*1*7+2+2^2+1+1=22. a(4)=2*1*22+2+2*2*7+2+1=77.
%p l:=1: : k := 1 : m :=2: d(0):=1:d(1):=m: for n from 1 to 32 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=0,34);seq(d(n),n=0..32);
%Y Cf. A176611.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 21 2010
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