login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112209 McKay-Thompson series of class 80a for the Monster group. 2
1, 1, 0, 1, 1, 2, 2, 1, 3, 3, 3, 3, 4, 5, 5, 7, 8, 8, 9, 10, 13, 15, 14, 17, 20, 23, 24, 26, 31, 34, 38, 41, 46, 52, 55, 62, 70, 75, 82, 90, 103, 112, 118, 131, 145, 161, 172, 185, 208, 225, 244, 265, 288, 316, 339, 370, 404, 435, 469, 507, 557, 601, 640, 696, 755, 818 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(Pi*sqrt(n/5)) / (2^(3/2) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

Expansion of q^(1/4)*(eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4)*eta(q^5) *eta(q^20)) in powers of q. - G. C. Greubel, Jun 20 2018

EXAMPLE

T80a = 1/q +q^3 +q^11 +q^15 +2*q^19 +2*q^23 +q^27 +3*q^31 +...

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[(1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/4)*(eta[q^2]*eta[q^10])^2/( eta[q]*eta[q^4]*eta[q^5]*eta[q^20]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jun 20 2018 *)

PROG

(PARI) q='q+O('q^70); Vec((eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4) *eta(q^5)*eta(q^20))) \\ G. C. Greubel, Jun 20 2018

CROSSREFS

Cf. A112182.

Sequence in context: A245325 A091224 A112182 * A240127 A109524 A191521

Adjacent sequences:  A112206 A112207 A112208 * A112210 A112211 A112212

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)