OFFSET
0,2
FORMULA
G.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) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +5*(-n+2)*a(n-3) +4*(-n+5)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 18 2016
EXAMPLE
a(2)=2*1*2+2-1=5. a(3)=2*1*5+2+2^2+1-1=16. a(4)=2*1*16+2+2*2*5+2-1=55.
MAPLE
l:=-1: : k := 1 : 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 : 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);
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 27 2010
STATUS
approved