%I #4 Mar 01 2016 16:14:28

%S 1,5,11,48,207,1016,5159,27337,148489,824232,4650657,26602827,

%T 153900879,898909266,5293577451,31395570786,187364023083,

%U 1124308178270,6779554362911,41059231942321,249646266800185,1523286825246798

%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*(-3*n+1)*a(n-1) +(-7*n+19)*a(n-2) +24*(n-3)*a(n-3) +12*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Mar 01 2016

%e a(2)=2*1*5+1=11. a(3)=2*1*11+5^2+1=48.

%p l:=1: : k := 0 : m :=5: d(0):=1:d(1):=m: for n from 1 to 28 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=0,31);seq(d(n),n=0..29);

%Y Cf. A176604, A176605, A176606, A176607.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, Apr 21 2010