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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058572 McKay-Thompson series of class 24B for Monster. 2
1, 0, 3, 8, 11, 16, 31, 40, 58, 96, 125, 176, 262, 336, 457, 640, 819, 1088, 1464, 1864, 2420, 3168, 3991, 5088, 6533, 8160, 10267, 12976, 16061, 19968, 24912, 30576, 37648, 46464, 56616, 69136, 84518, 102288, 123961, 150304, 180805, 217664, 262042, 313472 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of -2 + (eta(q^2)*eta(q^4)*eta(q^6)*eta(q^12)/(eta(q)*eta(q^3) *eta(q^8)*eta(q^24)))^2 in powers of q. - G. C. Greubel, Jan 28 2018

EXAMPLE

T24B = 1/q + 3*q + 8*q^2 + 11*q^3 + 16*q^4 + 31*q^5 + 40*q^6 + 58*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[-2 + (eta[q^2]*eta[q^4]*eta[q^6]*eta[q^12]/(eta[q]*eta[q^3]*eta[q^8] *eta[q^24]))^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 28 2018 *)

PROG

(PARI) q='q+O('q^50); A = -2 + (eta(q^2)*eta(q^4)*eta(q^6)*eta(q^12)/( eta(q)*eta(q^3)*eta(q^8)*eta(q^24)))^2/q; Vec(A) \\ G. C. Greubel, Jun 14 2018

CROSSREFS

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Cf. A212771 (same sequence except for n=0).

Sequence in context: A190435 A188032 A245978 * A310283 A262290 A184925

Adjacent sequences:  A058569 A058570 A058571 * A058573 A058574 A058575

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)