OFFSET
0,2
FORMULA
G.f. satisfies:
(1) Sum_{n>=0} 3^n * (1+x)^(n^2) / (3 + (1+x)^n)^(n+1).
(2) Sum_{n>=0} ((1+x)^n - 1/3)^n / 3.
EXAMPLE
G.f.: A(x) = 1 + 15*x + 786*x^2 + 69261*x^3 + 8554530*x^4 + 1359020643*x^5 + 263929299177*x^6 + 60582032629791*x^7 + 16046282916588207*x^8 + ...
such that
A(x) = 1/3 + (3*(1+x) - 1)/3^2 + (3*(1+x)^2 - 1)^3/3^3 + (3*(1+x)^3 - 1)^3/3^4 + (3*(1+x)^4 - 1)^4/3^5 + (3*(1+x)^5 - 1)^5/3^6 + ...
Also,
A(x) = 1/4 + 3*(1+x)/(3 + (1+x))^2 + 3^2*(1+x)^4/(3 + (1+x)^2)^3 + 3^3*(1+x)^9/(3 + (1+x)^3)^4 + 3^4*(1+x)^16/(3 + (1+x)^4)^5 + 3^5*(1+x)^25/(3 + (1+x)^5)^6 + 3^6*(1+x)^36/(3 + (1+x)^6)^7 + ...
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 14 2018
STATUS
approved