OFFSET
0,2
FORMULA
G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n * A(x)^n * (1+x)^(n^2) / (1 - x*(1+x)^n)^(n+1).
EXAMPLE
G.f.: A(x) = 1 + 2*x + 7*x^2 + 33*x^3 + 180*x^4 + 1071*x^5 + 6776*x^6 + 44907*x^7 + 308903*x^8 + 2192218*x^9 + 15986187*x^10 + ...
such that
A(x) = 1 + x*(1 + (1+x)*A(x)) + x^2*(1 + (1+x)^2*A(x))^2 + x^3*(1 + (1+x)^3*A(x))^3 + x^4*(1 + (1+x)^4*A(x))^4 + x^5*(1 + (1+x)^5*A(x))^5 + x^6*(1 + (1+x)^6*A(x))^6 + ...
Also,
A(x) = 1/(1-x) + x*A(x)*(1+x)/(1 - x*(1+x))^2 + x^2*A(x)^2*(1+x)^4/(1 - x*(1+x)^2)^3 + x^3*A(x)^3*(1+x)^9/(1 - x*(1+x)^3)^4 + x^4*A(x)^4*(1+x)^16/(1 - x*(1+x)^4)^5 + ...
PROG
(PARI) {a(n) = my(A=1); for(i=1, n, A = sum(m=0, n, x^m * (1 + A*(1+x +x*O(x^n))^m)^m ) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 25 2018
STATUS
approved