OFFSET
0,3
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4676*x^5/5! +...
where e.g.f. A = A(x) satisfies:
A(x) = 1 + ((1+x/2*A) + (-1+x/2*A)) +
1/2!*((1+x/2*A^2)^2 + 2*(1+x/2*A)*(-1+x/2*A) + (-1+x/2*A^2)^2) +
1/3!*((1+x/2*A^3)^3 + 3*(1+x/2*A^2)^2*(-1+x/2*A) + 3*(1+x/2*A)*(-1+x/2*A^2)^2 + (-1+x/2*A^3)^3) +
1/4!*((1+x/2*A^4)^4 + 4*(1+x/2*A^3)^3*(-1+x/2*A) + 6*(1+x/2*A^2)^2*(-1+x/2*A^2)^2 + 4*(1+x/2*A)*(-1+x/2*A^3)^3 + (-1+x/2*A^4)^4) +
1/5!*((1+x/2*A^5)^5 + 5*(1+x/2*A^4)^4*(-1+x/2*A) + 10*(1+x/2*A^3)^3*(-1+x/2*A^2)^2 + 10*(1+x/2*A^2)^2*(-1+x/2*A^3)^3 + 5*(1+x/2*A)*(-1+x/2*A^4)^4 + (-1+x/2*A^5)^5) +...
PROG
(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); for(i=1, n, A=1+sum(m=1, n, 1/m!*sum(k=0, m, binomial(m, k)*(1+X/2*A^(m-k))^(m-k)*(-1+X/2*A^k)^k))); n!*polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 26 2011
STATUS
approved