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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003295 McKay-Thompson series of class 11A for the Monster group with a(0) = -5.
(Formerly M3872)
3
1, -5, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

Coefficients of a modular function denoted by B(tau) in Atkin (1967).

REFERENCES

A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J., 8 (1967), 14-32.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=-1..30.

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, see p. 42.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

From Michael Somos, Aug 31 2012: (Start)

Expansion of -11 + (1 + 3*F)^2 * (1/F + 1 + 3*F) where F = eta(q^3) * eta(q^33) / (eta(q) * eta(q^11)) (= g.f. of A128663) in powers of q.

G.f. is Fourier series of a level 11 modular function. f(-1 / (11 t)) = f(t) where q = exp(2 Pi i t).

A000521(n) = a(n) + 11 * a(11*n) unless n=0. [Atkin (1967) p. 22]

a(n) = A003295(n) = A058205(n) = A128525(n) = A134784(n) unless n=0. (End)

EXAMPLE

G.f. = 1/q - 5 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...

MATHEMATICA

QP = QPochhammer; F = q*QP[q^3]*(QP[q^33]/(QP[q]*QP[q^11])); s = q*(-11 + (1 + 3*F)^2*(1/F + 1 + 3*F)) + O[q]^40; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 13 2015, from 1st formula *)

CROSSREFS

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

Cf. A003295, A058205, A128525, A128663, A134784.

Sequence in context: A146264 A146216 A046787 * A228857 A253427 A011853

Adjacent sequences:  A003292 A003293 A003294 * A003296 A003297 A003298

KEYWORD

sign,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 05 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 2 17:24 EST 2016. Contains 278682 sequences.