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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058557 McKay-Thompson series of class 20b for Monster. 1
1, 4, 3, 16, 20, 48, 55, 108, 141, 248, 326, 516, 662, 1048, 1335, 2000, 2547, 3672, 4689, 6588, 8379, 11500, 14513, 19644, 24688, 32896, 41115, 53964, 67301, 87312, 108385, 139124, 171876, 218852, 269284, 339996, 416665, 522104, 637698, 793704, 965989, 1194888, 1448933, 1782800 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3, in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T20b = 1/q + 4*q + 3*q^3 + 16*q^5 + 20*q^7 + 48*q^9 + 55*q^11 + 108*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^3; a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3; Vec(A + q/A) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A092398 A288199 A127675 * A287978 A288368 A288595

Adjacent sequences:  A058554 A058555 A058556 * A058558 A058559 A058560

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

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 22 11:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)