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!)
A058672 McKay-Thompson series of class 42B for Monster. 1
1, 0, 1, 0, 0, -2, 4, -2, 0, 0, 1, -4, 5, -4, 4, -2, 4, -10, 12, -12, 8, -4, 9, -16, 21, -22, 13, -8, 17, -32, 44, -40, 25, -24, 38, -56, 70, -66, 50, -44, 57, -92, 124, -116, 89, -80, 106, -164, 203, -188, 151, -132, 173, -264, 316, -298, 250, -230, 300 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,6

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of 2 + ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21))/(eta(q^2)* eta(q^3)*eta(q^7)*eta(q^42)))^2 in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/21)) / (2 * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T42B = 1/q + q - 2*q^4 + 4*q^5 - 2*q^6 + q^9 - 4*q^10 + 5*q^11 - 4*q^12 + ...

MATHEMATICA

eta[q_] := q^(1/24) * QPochhammer[q]; A := ((eta[q] * eta[q^6] * eta[q^14] * eta[q^21])/(eta[q^2] * eta[q^3] * eta[q^7] * eta[q^42]))^2; a := CoefficientList[Series[2 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 50}] (* G. C. Greubel, Jun 24 2018 *)

nmax = 60; CoefficientList[Series[2*x + Product[((1 + x^(3*k))*(1 + x^(7*k))/((1 + x^k)*(1 + x^(21*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 28 2018 *)

PROG

(PARI) q='q+O('q^70); F = 2 + ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21))/( eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2/q; Vec(F) \\ G. C. Greubel, Jun 24 2018

CROSSREFS

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

Sequence in context: A278886 A278887 A011168 * A278215 A317896 A320364

Adjacent sequences:  A058669 A058670 A058671 * A058673 A058674 A058675

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 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 19 16:32 EST 2019. Contains 319309 sequences. (Running on oeis4.)