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!)
A112173 McKay-Thompson series of class 36b for the Monster group. 3
1, 2, 1, 4, 8, 6, 10, 16, 18, 26, 33, 40, 58, 74, 82, 112, 147, 166, 212, 268, 316, 392, 476, 560, 695, 838, 967, 1184, 1430, 1648, 1970, 2352, 2731, 3236, 3803, 4404, 5206, 6080, 6984, 8192, 9553, 10942, 12709, 14736, 16886, 19506, 22448, 25648 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Convolution square of A112206. - Vaclav Kotesovec, Sep 08 2015
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(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2015
Expansion of q^(1/3)*((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)*eta(q^4)* eta(q^12)))^2 in powers of q. - G. C. Greubel, Jun 16 2018
Expansion of abs(q^(1/3)*(eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^2) in powers of q. - G. C. Greubel, Jun 16 2018
EXAMPLE
T36b = 1/q +2*q^2 +q^5 +4*q^8 +8*q^11 +6*q^14 +10*q^17 +...
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/3)*((eta[q^2]*eta[q^6])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^12]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)
PROG
(PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)* eta(q^4)*eta(q^12)))^2; Vec(A) \\ G. C. Greubel, Jun 16 2018
CROSSREFS
Cf. A112206.
Sequence in context: A158451 A257706 A118272 * A058543 A353661 A156817
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
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 April 20 22:14 EDT 2024. Contains 371848 sequences. (Running on oeis4.)