OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(2^n-1).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 105*x^5 + 556*x^6 +...
which satisfies:
A(x)^2 = A(x) + x*A(x)^2 + x^2*A(x)^4 + x^3*A(x)^8 + x^4*A(x)^16 +...
where:
A(x)^2 = 1 + 2*x + 5*x^2 + 16*x^3 + 62*x^4 + 280*x^5 + 1450*x^6 + 8626*x^7 +...
A(x)^4 = 1 + 4*x + 14*x^2 + 52*x^3 + 213*x^4 + 968*x^5 + 4896*x^6 + 27836*x^7 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*(A+x*O(x^n))^(2^m-1))); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 27 2011
STATUS
approved