%I #2 Mar 30 2012 18:37:12

%S 1,1,1,7,-11,741,-14129,521263,-20968359,1063764649,-63316356389,

%T 4408796480331,-352958649497387,32158017135672013,

%U -3302679619545572265,379346145007147112551,-48397471256028983134799,6817654800019973404119633,-1054828080584161260522077645

%N E.g.f. satisfies: A(x) = exp( A(x)*Series_Reversion[x*A(x)] ).

%F E.g.f. satisfies: A(x*A(x)) = exp(x*A(x*A(x))) = LambertW(-x)/(-x).

%e A(x) = 1 + x + x^2/2! + 7*x^3/3! - 11*x^4/4! + 741*x^5/5! - 14129*x^6/6! +-...

%e A(x*A(x)) = 1 + x + 3*x^2/2! + 16*x^3/3! + 125*x^4/4! + 1296*x^5/5! +...

%e LambertW(-x)/(-x) = 1 + x + 3^1*x^2/2! + 4^2*x^3/3! + 5^3*x^4/4! +...

%e log(A(x)) = x + 2*x^3/2! - 9*x^4/3! + 172*x^5/4! - 3205*x^6/5! +-...

%e Series_Reversion[x*A(x)] = x - x^2 + 3*x^3/2! - 22*x^4/3! + 281*x^5/4! - 5396*x^6/5! +-...

%o (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)}

%Y Cf. A000272.

%K sign

%O 0,4

%A _Paul D. Hanna_, Aug 26 2008