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!)
A112160 McKay-Thompson series of class 24E for the Monster group. 5
1, 4, 6, 8, 17, 28, 38, 56, 84, 124, 172, 232, 325, 448, 594, 784, 1049, 1388, 1796, 2320, 3005, 3864, 4912, 6216, 7877, 9940, 12430, 15488, 19309, 23972, 29580, 36408, 44766, 54876, 66978, 81536, 99150, 120272, 145374, 175344, 211242 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..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(Pi*sqrt(2*n/3)) / (2 * 6^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

Expansion of q^(1/6)*(eta(q^2)^2/(eta(q)*eta(q^4)))^4 in powers of q. - G. C. Greubel, Jan 25 2018

G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - (-x)^k))). - Ilya Gutkovskiy, Jun 07 2018

EXAMPLE

T24E = 1/q + 4*q^5 + 6*q^11 + 8*q^17 + 17*q^23 + 28*q^29 + 38*q^35 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k+1))^4, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)

eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/6)*(eta[q^2]^2/(eta[q]*eta[q^4]))^4, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 25 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)^2/(eta(q)*eta(q^4)))^4; Vec(A) \\ G. C. Greubel, Jul 01 2018

CROSSREFS

Sequence in context: A083166 A185292 A022599 * A132040 A210459 A279896

Adjacent sequences:  A112157 A112158 A112159 * A112161 A112162 A112163

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

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 23:12 EST 2019. Contains 319251 sequences. (Running on oeis4.)