OFFSET
1,3
COMMENTS
Compare g.f. to the identity (cf. A001710):
Sum_{n>=0} ( n*x/(1+n*x) )^n = 1 + Sum_{n>=1} (n+1)!/2 * x^n.
Also compare to the identity:
G(x) = x*Sum_{n>=0} G( x/(1+x) )^n is satisfied by: G(x) = x/(1-x).
EXAMPLE
G.f.: A(x) = x + x^2 + 4*x^3 + 30*x^4 + 372*x^5 + 6865*x^6 +...
where
A(x) = x + x*A(x/(1+x)) + x*A(2*x/(1+2*x))^2 + x*A(3*x/(1+3*x))^3 + x*A(4*x/(1+4*x))^4 + x*A(5*x/(1+5*x))^5 +...
PROG
(PARI) {a(n)=local(A=x); for(i=1, n, A=x*sum(m=0, n, subst(A, x, m*x/(1+m*x+x*O(x^n)))^m)); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 02 2013
STATUS
approved