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!)
A112221 McKay-Thompson series of class 120a for the Monster group. 1
1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 3, 2, 2, 3, 3, 4, 4, 3, 4, 6, 5, 5, 7, 7, 7, 9, 8, 9, 11, 10, 12, 14, 13, 14, 17, 18, 18, 20, 21, 23, 27, 25, 27, 33, 32, 34, 39, 39, 42, 46, 48, 51, 56, 57, 61, 71, 69, 72, 83, 85, 90, 97, 99, 108, 117, 119, 126, 140, 143, 149, 167, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of sqrt(T60B) in powers of q, where T60B = A058726. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(sqrt(2*n/15)*Pi) / (2^(5/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T120a = 1/q +q^5 +q^7 +q^9 +q^11 +q^15 +q^17 +q^19 +q^21 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q^2]*eta[q^6] *eta[q^10]*eta[q^30])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^5]*eta[q^12] *eta[q^15]*eta[q^20]*eta[q^60]); T60B := q*(B - 1);

a:= CoefficientList[Series[(T60B + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)

PROG

(PARI) q='q+O('q^80); B = (eta(q^2)*eta(q^6)*eta(q^10)*eta(q^30))^2/ (q*eta(q)*eta(q^3)*eta(q^4)*eta(q^5)*eta(q^12)*eta(q^15)*eta(q^20) *eta(q^60)); Vec(sqrt(q*(B - 1))) \\ G. C. Greubel, Jul 02 2018

CROSSREFS

Sequence in context: A263107 A286528 A112200 * A266697 A264402 A289186

Adjacent sequences:  A112218 A112219 A112220 * A112222 A112223 A112224

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 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)