OFFSET
0,3
COMMENTS
Compare to the identity:
Sum_{n>=0} n^n * x^n / (1 + n*x)^n = 1/2 + Sum_{n>=0} (n+1)!/2 * x^n.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 15*x^3 + 73*x^4 + 425*x^5 + 2908*x^6 +...
where
A(x) = 1 + x*(1+x)/(1+x) + x^2*(2+x)^2/(1+2*x)^2 + x^3*(3+x)^3/(1+3*x)^3 + x^4*(4+x)^4/(1+4*x)^4 + x^5*(5+x)^5/(1+5*x)^5 +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(m+x)^m/(1+m*x+x*O(x^n))^m), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 28 2013
STATUS
approved