OFFSET
0,3
FORMULA
G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=0} x^(2^n)*A(x)^(2^n)/(1 - x^(2^(n+1))).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 33*x^5 + 92*x^6 + 267*x^7 +...
The g.f. satisfies the following relations:
A(x) = 1 + x*A(x) + x^2*A(x)^2 + x^3*A(x) + x^4*A(x)^4 + x^5*A(x) + x^6*A(x)^2 + x^7*A(x) + x^8*A(x)^8 +...+ x^n*A(x)^A006519(n) +...
A(x) = 1 + x*A(x)/(1-x^2) + x^2*A(x)^2/(1-x^4) + x^4*A(x)^4/(1-x^8) + x^8*A(x)^8/(1-x^16) + x^16*A(x)^16/(1-x^32) +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*(A+x*O(x^n))^(2^valuation(m, 2)))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 16 2011
STATUS
approved