OFFSET
1,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..200
FORMULA
a(n) = [x^n] F_{n-1}(x) where F_n(x) = F_{n-1}(x+x^2) with F_1(x) = x+x^2 and F_0(x)=x for n>=1.
EXAMPLE
The iterations of (x+x^2) begin:
F(x) = x + (1)*x^2
F(F(x)) = x + 2*x^2 + (2)*x^3 + x^4
F(F(F(x))) = x + 3*x^2 + 6*x^3+ (9)*x^4 +...
F(F(F(F(x)))) = x + 4*x^2 + 12*x^3 + 30*x^4 + (64)*x^5 +...
F(F(F(F(F(x))))) = x + 5*x^2 + 20*x^3 + 70*x^4 + 220*x^5 + (630)*x^6 +...
coefficients enclosed in parenthesis form the initial terms of this sequence.
PROG
(PARI) {a(n)=local(F=x+x^2, G=x+x*O(x^n)); if(n<1, 0, for(i=1, n-1, G=subst(F, x, G)); return(polcoeff(G, n, x)))}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 06 2005
STATUS
approved