OFFSET
1,3
FORMULA
G.f. satisfies: A(x) = x + x^2 * A'(x) * A'(A(x)).
EXAMPLE
G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 324*x^5 + 4480*x^6 + 74544*x^7 +...
Related expansions:
A'(x) = 1 + 2*x + 12*x^2 + 120*x^3 + 1620*x^4 + 26880*x^5 + 521808*x^6 +...
A(A(x)) = x + 2*x^2 + 10*x^3 + 81*x^4 + 896*x^5 + 12424*x^6 + 205544*x^7 +...
PROG
(PARI) {a(n)=local(A=x+x^2+x*O(x^n)); for(i=1, n, A=x+x^2*deriv(subst(A, x, A))); polcoeff(A, n)}
for(n=1, 21, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 21 2012
STATUS
approved