OFFSET
2,3
FORMULA
G.f. satisfies: A(x) = ( A(x)^3 + A(A(A(x))) ) / A(A(x)).
EXAMPLE
G.f.: A(x) = x^2 + x^3 + 2*x^4 + 6*x^5 + 19*x^6 + 65*x^7 + 231*x^8 +...
such that
A(A(x)) = x^4 + 2*x^5 + 6*x^6 + 19*x^7 + 65*x^8 + 231*x^9 +...+ a(n+1)*x^(n+2) +...
Related expansions:
A(A(A(x))) = x^8 + 4*x^9 + 16*x^10 + 62*x^11 + 243*x^12 + 956*x^13 +...
A(x)^3 = x^6 + 3*x^7 + 9*x^8 + 31*x^9 + 111*x^10 + 411*x^11 + 1556*x^12 +...
A(x)*A(A(x)) = x^6 + 3*x^7 + 10*x^8 + 35*x^9 + 127*x^10 + 473*x^11 + 1799*x^12 +...
where A(x)*A(A(x)) = A(x)^3 + A(A(A(x))).
PROG
(PARI) {a(n)=local(A=x^2+x^3); for(i=1, n, A=x^2+subst(A, x, A+x*O(x^n))/x); polcoeff(A, n)}
for(n=2, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 11 2012
STATUS
approved