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A317799 G.f.: Sum_{n>=0} (4*(1+x)^n - 1)^n / 4^(n+1). 1

%I

%S 1,28,2644,418108,92624756,26388012380,9189259388052,3782063138596476,

%T 1796136011427955636,966755321167565129372,581573928178258915024596,

%U 386690499153558305585430460,281600848152507182372274325492,222904650325844057584524049181660,190559248618061561787517993382005012

%N G.f.: Sum_{n>=0} (4*(1+x)^n - 1)^n / 4^(n+1).

%F G.f. satisfies:

%F (1) Sum_{n>=0} 4^n * (1+x)^(n^2) / (4 + (1+x)^n)^(n+1).

%F (2) Sum_{n>=0} ((1+x)^n - 1/4)^n / 4.

%e 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 + ...

%e such that

%e 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 + ...

%e Also,

%e 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 + ...

%Y Cf. A122400, A301463, A317798, A301583.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 14 2018

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Last modified October 3 15:08 EDT 2022. Contains 357237 sequences. (Running on oeis4.)