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!)
A058516 McKay-Thompson series of class 16C for Monster. 4
1, 0, 8, 16, 34, 64, 112, 192, 319, 512, 808, 1248, 1886, 2816, 4144, 6016, 8643, 12288, 17296, 24144, 33442, 45952, 62720, 85056, 114620, 153600, 204728, 271456, 358204, 470528, 615344, 801408, 1039621, 1343488, 1729920, 2219808, 2838920, 3619136, 4599664 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
COMMENTS
A058516, A176143, A214035, A215346 are all essentially the same sequence. - N. J. A. Sloane, Aug 08 2012
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
a(n) ~ exp(sqrt(n)*Pi) / (2^(3/2) * n^(3/4)). - Vaclav Kotesovec, May 01 2017
Expansion of eta(q^4)^10/(eta(q)^2 *eta(q^2)^3 *eta(q^8)^3* eta(q^16)^2)) - 2 in powers of q. - G. C. Greubel, May 28 2018
Expansion of -2 + (1/q) * chi(q)^2 * chi(q^2)^7 * chi(q^4)^2 in powers of q where chi() is a Ramanujan theta function. - Michael Somos, Feb 09 2019
EXAMPLE
T16C = 1/q + 8*q + 16*q^2 + 34*q^3 + 64*q^4 + 112*q^5 + 192*q^6 + 319*q^7 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A058516:= CoefficientList[Series[ q*(-2 + eta[q^4]^10/(eta[q]^2 *eta[q^2]^3 *eta[q^8]^3* eta[q^16]^2)), {q, 0, 60}], q]; Table[A058516[[n]], {n, 1, 50}] (* G. C. Greubel, May 28 2018 *)
a[ n_] := SeriesCoefficient[ -2 + q^-1 QPochhammer[ -q, q^2]^2 QPochhammer[ -q^2, q^4]^7 QPochhammer[ -q^4, q^8]^2, {q, 0, n}]; (* Michael Somos, Feb 09 2019 *)
PROG
(PARI) q='q+O('q^30); {h = (1/q)*(eta(q^4)^10/(eta(q)^2*eta(q^2)^3 *eta(q^8)^3*eta(q^16)^2))}; Vec(-2 + h) \\ G. C. Greubel, May 28 2018
CROSSREFS
Cf. A176143, A214035 (same sequence except for n=0).
Sequence in context: A331930 A072578 A271994 * A366511 A217672 A194601
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
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 March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)