OFFSET
0,3
FORMULA
G.f.: Sum_{n>=0} x^n * Sum{k=0..n} a(k)*(n-k)^k/(1 - (n-k)*x)^k = Sum_{n>=0} a(n)*x^n.
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 27*x^4 + 172*x^5 + 1508*x^6 +...
where
A(x) = 1 + A(x/(1-x))*x + A(2*x/(1-2*x))*x^2 + A(3*x/(1-3*x))*x^3 + A(4*x/(1-4*x))*x^4 + A(5*x/(1-5*x))*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, subst(A, x, m*x/(1-m*x+x*O(x^n)))*x^m)); polcoeff(A, n)}
for(n=0, 21, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 19 2013
STATUS
approved