The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A358952 a(n) = coefficient of x^n in A(x) such that: 0 = Sum_{n=-oo..+oo} x^(2*n) * (x^n - 2*A(x))^(3*n+1). 9
1, 2, 18, 124, 1244, 11652, 122153, 1281722, 14009973, 154993908, 1748602308, 19949674928, 230299666100, 2682127476280, 31492460744869, 372295036400060, 4428101312591810, 52949362040059258, 636176332781478365, 7676183282453865394, 92978971123440688904 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Related identity: 0 = Sum_{n=-oo..+oo} x^n * (y - x^n)^n, which holds formally for all y.
LINKS
FORMULA
G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies:
(1) 0 = Sum_{n=-oo..+oo} x^(2*n) * (x^n - 2*A(x))^(3*n+1).
(2) 0 = Sum_{n=-oo..+oo} x^(3*n*(n-1)) / (1 - 2*A(x)*x^n)^(3*n-1).
a(n) ~ c * d^n / n^(3/2), where d = 13.043520100475... and c = 0.432996977380... - Vaclav Kotesovec, Dec 08 2022
EXAMPLE
G.f.: A(x) = 1 + 2*x + 18*x^2 + 124*x^3 + 1244*x^4 + 11652*x^5 + 122153*x^6 + 1281722*x^7 + 14009973*x^8 + 154993908*x^9 + 1748602308*x^10 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(n=-#A, #A, x^(2*n) * (x^n - 2*Ser(A))^(3*n+1) ), #A-1)/2); A[n+1]}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A342124 A289830 A361304 * A060589 A325275 A277661
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 07 2022
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 May 22 14:42 EDT 2024. Contains 372755 sequences. (Running on oeis4.)