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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058743 McKay-Thompson series of class 69A for Monster. 1
1, 0, 1, 1, 1, 1, 3, 2, 2, 4, 4, 4, 7, 6, 8, 10, 10, 11, 16, 15, 18, 22, 24, 26, 34, 34, 39, 47, 50, 56, 69, 70, 80, 93, 100, 110, 131, 137, 154, 176, 189, 208, 241, 254, 283, 320, 345, 377, 430, 456, 505, 563, 607, 661, 744, 793, 871, 964, 1039, 1129, 1257 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,7

COMMENTS

Also McKay-Thompson series of class 69B for Monster. - Michel Marcus, Feb 24 2014

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = -1..10000 (terms -1..2500 from G. C. Greubel)

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 -1 + A*B/q, where A = G(q^69)*G(q) + q^14*H(q^69)*H(q), B = G(q^23)*H(q^3) - q^4*H(q^23)*G(q^3), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(4*Pi*sqrt(n/69)) / (sqrt(2) * 69^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T69A = 1/q + q + q^2 + q^3 + q^4 + 3*q^5 + 2*q^6 + 2*q^7 + 4*q^8 + 4*q^9 + ...

MATHEMATICA

QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A:= G[x^69]*G[x] + x^14*H[x^69]*H[x]; B:= G[x^23]*H[x^3] - x^4*H[x^23]*G[x^3]; a:= CoefficientList[Series[-1*x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018 *)

CROSSREFS

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

Sequence in context: A287870 A308190 A235354 * A117970 A298904 A308194

Adjacent sequences:  A058740 A058741 A058742 * A058744 A058745 A058746

KEYWORD

nonn

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 October 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)