OFFSET
1,3
FORMULA
G.f. satisfies: A( x - A(A(A(x)))^2 ) = x.
EXAMPLE
G.f.: A(x) = x + x^2 + 8*x^3 + 104*x^4 + 1724*x^5 + 33280*x^6 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 18*x^3 + 249*x^4 + 4304*x^5 + 85740*x^6 +...
A(A(A(x))) = x + 3*x^2 + 30*x^3 + 441*x^4 + 7958*x^5 + 163940*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 44*x^3 + 686*x^4 + 12928*x^5 + 275758*x^6 +...
A(A(A(A(x))))^2 = x^2 + 8*x^3 + 104*x^4 + 1724*x^5 + 33280*x^6 +...
The series reversion of A(x) = x - A(A(A(x)))^2, where
A(A(A(x)))^2 = x^2 + 6*x^3 + 69*x^4 + 1062*x^5 + 19462*x^6 + 402088*x^7 +...
PROG
(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A^2, x, subst(A, x, subst(A, x, A+x*O(x^n))))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 28 2008
STATUS
approved