OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = G(x/A(x)) where A(x*G(x)) = G(x) = Sum_{n>=0} n!^2*x^n.
G.f. satisfies: [x^n] A(x)^(n+1)/(n+1) = n!^2.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 26*x^3 + 435*x^4 + 11454*x^5 +...
G.f. satisfies A(x) = G(x/A(x)) where A(x*G(x)) = G(x) begins:
G(x) = 1 + x + 2!^2*x^2 + 3!^2*x^3 + 4!^2*x^4 + 5!^2*x^5 +...
so that:
A(x) = 1 + x/A(x) + 2!^2*x^2/A(x)^2 + 3!^2*x^3/A(x)^3 + 4!^2*x^4/A(x)^4 +...
PROG
(PARI) {a(n)=polcoeff(x/serreverse(sum(m=1, n+1, (m-1)!^2*x^m)+x^2*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 31 2010
STATUS
approved