OFFSET
0,3
COMMENTS
Compare to the identity: 1/(1-x) = Sum_{n>=0} n^n*x^n/n! * exp(-n*x).
EXAMPLE
G.f.: A(x) = 1 + x + 5*x^2 + 60*x^3 + 1539*x^4 + 82539*x^5 + 9208086*x^6 +...
where
1+x = 1 + x*A(-x)*exp(-x*A(-x)) + 2^2*x^2*A(-2*x)^2/2!*exp(-2*x*A(-2*x)) + 3^3*x^3*A(-3*x)^3/3!*exp(-3*x*A(-3*x)) + 4^4*x^4*A(-4*x)^4/4!*exp(-4*x*A(-4*x)) +...
PROG
(PARI) a(n)=local(A=1+x+sum(k=2, n-1, a(k)*x^k)+x^2*O(x^n)); if(n<2, 1, -(-1)^n*polcoeff(sum(k=0, n+2, k^k*x^k*subst(A, x, -k*x)^k/k!*exp(-k*x*subst(A, x, -k*x)+x^2*O(x^n))), n+1))
for(n=0, 15, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 06 2012
STATUS
approved