OFFSET
0,3
FORMULA
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).
Conjecture: (n+1)*a(n) +(2-7n)*a(n-1) +(19n-29)*a(n-2) +(110-37n)*a(n-3) +36*(n-4)*a(n-4) +12*(5-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011
EXAMPLE
a(2)=(1*0+1)+(1*0+1)+1=3. a(3)=2*1*3+2+(0^2+1)+1=10. a(4)=2*1*10+2+2*0*3+2+1=25.
MAPLE
l:=1: : k := 1 : m:=0: 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 :
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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Choulet, Apr 21 2010
STATUS
approved