OFFSET
1,3
EXAMPLE
A(x) = x - x^2/(1!*2!) + 5*x^3/(1!*2!*3!) - 121*x^4/(1!*2!*3!*4!) + 16199*x^5/(1!*2!*3!*4!*5!) - 13857481*x^6/(1!*2!*3!*4!*5!*6!) +...+ a(n)*x^n/sf(n) +...
where
1+x = 1 + A(x) + A(x)^2/(1!*2!) + A(x)^3/(1!*2!*3!) + A(x)^4/(1!*2!*3!*4!) + A(x)^5/(1!*2!*3!*4!*5!) + A(x)^6/(1!*2!*3!*4!*5!*6!) +...+ A(x)^n/sf(n) +...
and sf(n) = 0!*1!*2!*3!*...*(n-1)!*n!.
PROG
(PARI) {a(n)=local(A=sum(m=1, n-1, a(m)*x^m/prod(k=0, m, k!))+O(x^(n+2)));
prod(k=0, n, k!)*polcoeff(1+x-sum(m=0, n, A^m/prod(k=0, m, k!)), n)}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jul 27 2011
STATUS
approved