login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317799 G.f.: Sum_{n>=0} (4*(1+x)^n - 1)^n / 4^(n+1). 1
1, 28, 2644, 418108, 92624756, 26388012380, 9189259388052, 3782063138596476, 1796136011427955636, 966755321167565129372, 581573928178258915024596, 386690499153558305585430460, 281600848152507182372274325492, 222904650325844057584524049181660, 190559248618061561787517993382005012 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

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

Cf. A122400, A301463, A317798, A301583.

Sequence in context: A281137 A100548 A103660 * A275654 A283519 A284770

Adjacent sequences:  A317796 A317797 A317798 * A317800 A317801 A317802

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 14 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 17 17:59 EDT 2022. Contains 356189 sequences. (Running on oeis4.)