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!)
A058729 McKay-Thompson series of class 60E for the Monster group. 2
1, 1, 1, 1, 1, 3, 3, 4, 4, 4, 7, 8, 10, 11, 12, 16, 18, 22, 25, 28, 34, 38, 45, 51, 58, 69, 77, 88, 99, 112, 131, 146, 165, 184, 206, 238, 266, 298, 331, 368, 418, 465, 520, 576, 637, 714, 791, 880, 973, 1074, 1194, 1316, 1455, 1604, 1766, 1954, 2145, 2360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

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 chi(-x^3) * chi(-x^15) / (chi(-x) * chi(-x^5)) in powers of x where chi() is a Ramanujan theta function. - Michael Somos, Jun 09 2012

G.f. is a period 1 Fourier series which satisfies f(-1 / (120 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Jun 09 2012

Convolution square is A205962. - Michael Somos, Jun 09 2012

a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 06 2015

Expansion of q^(1/2)*eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30)) in powers of q. - G. C. Greubel, Jun 19 2018

EXAMPLE

1 + x + x^2 + x^3 + x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 4*x^8 + 4*x^9 + 7*x^10 + ...

T60E = 1/q + q + q^3 + q^5 + q^7 + 3*q^9 + 3*q^11 + 4*q^13 + 4*q^15 + 4*q^17 + ...

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x^k) * (1 + x^(5*k)) / ((1 + x^(3*k)) * (1 + x^(15*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 06 2015 *)

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)* eta[q^2]*eta[q^3]*eta[q^10]*eta[q^15]/(eta[q]* eta[q^5]*eta[q^6] *eta[q^30]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^10 + A) * eta(x^15 + A) / (eta(x + A) * eta(x^5 + A) * eta(x^6 + A) * eta(x^30 + A)), n))} /* Michael Somos, Jun 09 2012 */

CROSSREFS

Cf. A205962.

Sequence in context: A136546 A278765 A210881 * A021303 A303821 A240622

Adjacent sequences:  A058726 A058727 A058728 * A058730 A058731 A058732

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

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 18:37 EST 2019. Contains 319251 sequences. (Running on oeis4.)