OFFSET
1,3
FORMULA
G.f. satisfies: A( x - A(A(A(x))^2) ) = x.
EXAMPLE
G.f.: A(x) = x + x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...
Related expansions:
A(A(x)) = x + 2*x^2 + 14*x^3 + 147*x^4 + 1890*x^5 + 27732*x^6 +...
A(A(A(x))) = x + 3*x^2 + 24*x^3 + 273*x^4 + 3730*x^5 + 57488*x^6 +...
A(A(A(A(x)))) = x + 4*x^2 + 36*x^3 + 442*x^4 + 6412*x^5 + 103890*x^6 +...
A(A(A(A(x)))^2) = x^2 + 6*x^3 + 58*x^4 + 702*x^5 + 9830*x^6 +...
The series reversion of A(x) = x - A(A(A(x))^2), where
A(A(A(x))^2) = x^2 + 4*x^3 + 33*x^4 + 358*x^5 + 4650*x^6 + 68168*x^7 +...
PROG
(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+subst(A, x, subst(A^2, x, subst(A, x, A+x*O(x^n))))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 28 2008
STATUS
approved