OFFSET
0,3
COMMENTS
Compare to: W(x) = Sum_{n>=0} x^n * exp(n*x*W(x)) / n! where W(x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!.
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 149*x^4/4! + 2196*x^5/5! +...
where
A(x) = 1 + x*exp(x*A(x)) + x^2*exp(2*x*A(2*x))/2! + x^3*exp(3*x*A(3*x))/3! + x^4*exp(4*x*A(4*x))/4! +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/m!*exp(m*x*subst(A, x, m*x)+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 16 2013
STATUS
approved
