OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..50
FORMULA
G.f.: 1 = Sum_{n>=0} 3^n * (1+x)^(n^2) / (3 + (1+x)^n * A(x))^(n+1).
EXAMPLE
G.f.: A(x) = 1 + 15*x + 291*x^2 + 20868*x^3 + 2501535*x^4 + 406641390*x^5 + 82021892979*x^6 + 19576367780568*x^7 + 5370958558206975*x^8 + ...
such that
1 = 1/3 + (3*(1+x) - A(x))/3^2 + (3*(1+x)^2 - A(x))^2/3^3 + (3*(1+x)^3 - A(x))^3/3^4 + (3*(1+x)^4 - A(x))^4/3^5 + (3*(1+x)^5 - A(x))^5/3^6 + ...
Also,
1 = 1/(3 + A(x)) + 3*(1+x)/(3 + (1+x)*A(x))^2 + 3^2*(1+x)^4/(3 + (1+x)^2*A(x))^3 + 3^3*(1+x)^9/(3 + (1+x)^3*A(x))^4 + 3^4*(1+x)^16/(3 + (1+x)^4*A(x))^5 + 3^5*(1+x)^25/(3 + (1+x)^5*A(x))^6 + ...
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 28 2018
STATUS
approved