OFFSET
0,2
FORMULA
G.f. satisfies:
(1) Sum_{n>=0} 4^n * (1+x)^(n^2) / (4 + (1+x)^n)^(n+1).
(2) Sum_{n>=0} ((1+x)^n - 1/4)^n / 4.
EXAMPLE
G.f.: A(x) = 1 + 28*x + 2644*x^2 + 418108*x^3 + 92624756*x^4 + 26388012380*x^5 + 9189259388052*x^6 + 3782063138596476*x^7 + 1796136011427955636*x^8 + ...
such that
A(x) = 1/4 + (4*(1+x) - 1)/4^2 + (4*(1+x)^2 - 1)^3/4^3 + (4*(1+x)^3 - 1)^4/4^4 + (4*(1+x)^4 - 1)^4/4^5 + (4*(1+x)^5 - 1)^5/4^6 + ...
Also,
A(x) = 1/5 + 4*(1+x)/(4 + (1+x))^2 + 4^2*(1+x)^4/(4 + (1+x)^2)^4 + 4^3*(1+x)^9/(4 + (1+x)^3)^4 + 4^4*(1+x)^16/(4 + (1+x)^4)^5 + 4^5*(1+x)^25/(4 + (1+x)^5)^6 + 4^6*(1+x)^36/(4 + (1+x)^6)^7 + ...
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 14 2018
STATUS
approved