OFFSET
0,2
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) +(2-7*n)*a(n-1) +3*(17-7*n)*a(n-2) +(91*n-278)*a(n-3) +4*(101-25*n)*a(n-4) +36*(n-5)*a(n-5)=0. - R. J. Mathar, Jul 24 2012
MAPLE
l:=-1: : k := 1 : for m from 0 to 10 do 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 :
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): od;
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, May 04 2010
STATUS
approved