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%I #6 Oct 08 2016 09:13:09
%S 1,5,9,42,173,846,4177,21691,114911,622910,3428951,19138401,108003785,
%T 615344844,3534413525,20444816044,118994823449,696370777980,
%U 4095034311841,24185709305851,143402427296079,853276282454676
%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=0 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=0, l=-1).
%F Conjecture: (n+1)*a(n) +2(1-3n)*a(n-1) +(19-7n)*a(n-2) +4*(8n-25)*a(n-3) +20(4-n)*a(n-4)=0. - _R. J. Mathar_, Nov 27 2011
%e a(2)=2*1*5-1=9. a(3)=2*1*9+5^2-1=42. a(4)=2*1*42+2*5*9-1=173.
%p l:=-1: : k := 0 : m:=2: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. A176750.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Apr 25 2010
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