OFFSET
1,3
EXAMPLE
G.f.: A(x) = x + x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 26*x^6 + 72*x^7 +...
A((x+x^2)*A(x)) = x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 26*x^6 + 72*x^7 +...
Let G(x) = (x+x^2)*A(x) then
A(x) = x + G(x) + G(G(x)) + G(G(G(x))) + G(G(G(G(x)))) + ... where
G(x) = x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 14*x^6 + 36*x^7 + 98*x^8 +...;
G(G(x)) = x^4 + 4*x^5 + 12*x^6 + 36*x^7 + 106*x^8 + 312*x^9 +...;
G(G(G(x))) = x^8 + 8*x^9 + 40*x^10 + 168*x^11 + 646*x^12 +...;
G(G(G(G(x)))) = x^16 + 16*x^17 + 144*x^18 + 976*x^19 +...; ...
PROG
(PARI) {a(n)=local(A=x+x*O(x)); for(i=0, n, A=x+subst(A, x, x*(1+x)*A)); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 16 2009
STATUS
approved