OFFSET
1,4
EXAMPLE
G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 11*x^5 + 126*x^6 + 2383*x^7 +...
where
A(A(x)) = x*(1+x) + x^2*(1+x)*(1+2*x) + x^3*(1+x)*(1+2*x)*(1+3*x) + 2*x^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x) + 11*x^5*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x) +...
Explicitly,
A(A(x)) = x + 2*x^2 + 4*x^3 + 10*x^4 + 42*x^5 + 367*x^6 + 6064*x^7 +...
PROG
(PARI) {a(n)=local(A=[1], F=x, G=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A);
G=sum(m=1, #A-1, A[m]*x^m*prod(k=1, m, 1+k*x +x*O(x^#A)) );
A[#A]=Vec(G)[#A]-Vec(subst(F, x, F))[#A]); if(n<1, 0, A[n])}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 19 2011
STATUS
approved