OFFSET
0,4
FORMULA
E.g.f. satisfies: A(x*A(x)) = exp(x*A(x*A(x))) = LambertW(-x)/(-x).
EXAMPLE
A(x) = 1 + x + x^2/2! + 7*x^3/3! - 11*x^4/4! + 741*x^5/5! - 14129*x^6/6! +-...
A(x*A(x)) = 1 + x + 3*x^2/2! + 16*x^3/3! + 125*x^4/4! + 1296*x^5/5! +...
LambertW(-x)/(-x) = 1 + x + 3^1*x^2/2! + 4^2*x^3/3! + 5^3*x^4/4! +...
log(A(x)) = x + 2*x^3/2! - 9*x^4/3! + 172*x^5/4! - 3205*x^6/5! +-...
Series_Reversion[x*A(x)] = x - x^2 + 3*x^3/2! - 22*x^4/3! + 281*x^5/4! - 5396*x^6/5! +-...
PROG
(PARI) {a(n)=local(A=1); for(i=0, n, A=exp(A*serreverse(x*A+x^2*O(x^n)))); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Aug 26 2008
STATUS
approved