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!)
A007255 McKay-Thompson series of class 6B for Monster.
(Formerly M5354)
3
1, 0, 78, 364, 1365, 4380, 12520, 32772, 80094, 185276, 409578, 871272, 1792754, 3582708, 6977100, 13277472, 24747867, 45267324, 81389908, 144048396, 251265288, 432425864, 734953116, 1234647216, 2051576037 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
I. Chen and N. Yui, Singular values of Thompson series. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
a(n) = A045485(n) = A121665(n) apart from n=0. - Sean A. Irvine, Nov 26 2017
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
EXAMPLE
T6B = 1/q + 78*q + 364*q^2 + 1365*q^3 + 4380*q^4 + 12520*q^5 + 32772*q^6 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-12 + (eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^12), {q, 0, 60}], q];
Table[A007255[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 12 2018 *)
PROG
(PARI) q='q+O('q^30); A=-12+(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12/q; Vec(A) \\ G. C. Greubel, Jun 12 2018
CROSSREFS
Sequence in context: A317412 A231393 A231461 * A003913 A251321 A074089
KEYWORD
nonn
AUTHOR
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 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)