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!)
A058615 McKay-Thompson series of class 30D for Monster. 2
1, 0, 3, 4, 5, 10, 15, 22, 29, 36, 53, 72, 99, 128, 160, 212, 272, 354, 448, 556, 703, 874, 1096, 1356, 1662, 2050, 2501, 3060, 3716, 4492, 5444, 6550, 7882, 9436, 11262, 13460, 16013, 19034, 22536, 26616, 31450, 37048, 43602, 51164, 59905 (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

Expansion of -2 + ((eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15))/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30)))^2 in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T30D = 1/q + 3*q + 4*q^2 + 5*q^3 + 10*q^4 + 15*q^5 + 22*q^6 + 29*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^2]*eta[q^3]*eta[q^10]* eta[q^15])/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30]))^2; a:= CoefficientList[Series[-2 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = -2 + ((eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15))/( eta(q)* eta(q^5)*eta(q^6)*eta(q^30)))^2/q; Vec(A) \\ G. C. Greubel, Jun 18 2018

CROSSREFS

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

Cf. A205962 (same sequence except for n=0).

Sequence in context: A079351 A183050 A176848 * A082612 A170926 A122413

Adjacent sequences:  A058612 A058613 A058614 * A058616 A058617 A058618

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 January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)