OFFSET
0,3
FORMULA
G.f. satisfies: A(x) = Sum_{n>=0} 2^n*x^n * A(x)^(n^2)/(1 + x*A(x)^n)^(n+1).
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 93*x^4 + 655*x^5 + 5025*x^6 +...
where the g.f. satisfies following series identity:
A(x) = 1 + (2*A(x)-1)*x + (2*A(x)^2-1)^2*x^2 + (2*A(x)^3-1)^3*x^3 + (2*A(x)^4-1)^4*x^4 +...
A(x) = 1/(1+x) + 2*x*A(x)/(1+x*A(x))^2 + 2^2*x^2*A(x)^4/(1+x*A(x)^2)^3 + 2^3*x^3*A(x)^9/(1+x*A(x)^3)^4 + 2^4*x^4*A(x)^16/(1+x*A(x)^4)^5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, (2*A^k-1+x*O(x^n))^k*x^k)); polcoeff(A, n)}
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, 2^k*A^(k^2)*x^k/(1+A^k*x+x*O(x^n))^(k+1) )); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 27 2011
STATUS
approved