OFFSET
1,3
COMMENTS
Compare to g.f. G(x) = x + x*G(G(x)) of A030266, where:
G(x) = x + x*Sum{n>=0} x^n/n! * d^n/dx^n G(x)^(n+1)/(n+1).
EXAMPLE
G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 62*x^5 + 377*x^6 + 2585*x^7 +...
where
A(x) = x + x*A(x)/0! + x^2*d/dx A(x)^2/1! + x^3*d^2/dx^2 A(x)^3/2! + x^4*d^3/dx^3 A(x)^4/3! + x^5*d^4/dx^4 A(x)^5/4! +...
PROG
(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}
{a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x+x*sum(m=0, n, x^m/m!*Dx(m, (A+x*O(x^n))^(m+1)) )); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 27 2012
STATUS
approved