OFFSET
0,2
FORMULA
G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2) * (1 + 1/A(x)^(2*n))^n.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 88*x^4 + 624*x^5 + 4112*x^6 +...
where
A(x) = 1 + x*(A(x)+1/A(x)) + x^2*(A(x)^2+1/A(x)^2)^2 + x^3*(A(x)^3+1/A(x)^3)^3 + x^4*(A(x)^4+1/A(x)^4)^4 +...
A(x)+1/A(x) = 2 + 4*x^2 + 8*x^3 + 32*x^4 + 304*x^5 + 2160*x^6 +...
(A(x)^2+1/A(x)^2)^2 = 4 + 64*x^2 + 128*x^3 + 832*x^4 + 6144*x^5 +...
(A(x)^3+1/A(x)^3)^3 = 8 + 432*x^2 + 864*x^3 + 12384*x^4 + 68544*x^5 +...
(A(x)^4+1/A(x)^4)^4 = 16 + 2048*x^2 + 4096*x^3 + 124928*x^4 + 589824*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=sum(m=0, n, x^m*(A^m+1/A^m)^m)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 26 2012
STATUS
approved