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!)
A181977 Expansion of b(q) * c(q^3)^2 / 9 in powers of q where b(), c() are cubic AGM theta functions. 1
1, -3, 0, 8, -9, 0, 17, -27, 0, 40, -39, 0, 50, -72, 0, 96, -81, 0, 104, -150, 0, 176, -153, 0, 170, -243, 0, 280, -216, 0, 273, -360, 0, 400, -351, 0, 362, -510, 0, 560, -450, 0, 520, -648, 0, 736, -615, 0, 601, -864, 0, 936, -729, 0, 850, -1086, 0, 1160 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882).
LINKS
FORMULA
Expansion of (eta(q) * eta(q^9)^2 / eta(q^3))^3 in powers of q.
Euler transform of period 9 sequence [-3, -3, 0, -3, -3, 0, -3, -3, -6, ...].
a(3*n + 1) = 0. a(3*n) = -3 * A106402(n).
EXAMPLE
G.f. = q^2 - 3*q^3 + 8*q^5 - 9*q^6 + 17*q^8 - 27*q^9 + 40*q^11 - 39*q^12 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[(eta[q]* eta[q^9]^2/eta[q^3])^3, {q, 0, 50}], q] (* G. C. Greubel, Aug 11 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<2, 0, n = n-2; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^9 + A)^2 / eta(x^3 + A))^3, n))};
CROSSREFS
Cf. A106402.
Sequence in context: A189969 A021768 A155876 * A199659 A201584 A281298
KEYWORD
sign
AUTHOR
Michael Somos, Apr 04 2012
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 June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)