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!)
A187147 McKay-Thompson series of class 12B for the Monster group with a(0) = -4. 3
1, -4, 6, -4, -3, 12, -8, -12, 30, -20, -30, 72, -46, -60, 156, -96, -117, 300, -188, -228, 552, -344, -420, 1008, -603, -732, 1770, -1048, -1245, 2976, -1776, -2088, 4908, -2900, -3420, 7992, -4658, -5460, 12756, -7408, -8583, 19944, -11564, -13344, 30756 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=-1..43.

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of (1/q) * (psi(-q) / psi(-q^3))^4 in powers of q.

Expansion of (eta(q) * eta(q^4) * eta(q^6) / (eta(q^2) * eta(q^3) * eta(q^12)))^4 in powers of q.

Euler transform of period 12 sequence [ -4, 0, 0, -4, -4, 0, -4, -4, 0, 0, -4, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = 9 / f(t) where q = exp(2 Pi i t).

Convolution square of A062243.

G.f.: ( Product_{k>0} (1 - x^(4*k)) * (1 - x^(2*k-1)) / (1 - x^(3*k)) )^4.

EXAMPLE

G.f. = 1/q - 4 + 6*q - 4*q^2 - 3*q^3 + 12*q^4 - 8*q^5 - 12*q^6 + 30*q^7 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (EllipticTheta[ 2, Pi/4, q^(1/2)] / EllipticTheta[ 2, Pi/4, q^(3/2)])^4, {q, 0, n}]; (* Michael Somos, Sep 05 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) / (eta(x^2 + A) * eta(x^3 + A) * eta(x^12 + A)))^4, n))};

CROSSREFS

Cf. A062243, A112148.

Sequence in context: A204693 A204817 A199721 * A128633 A001482 A198493

Adjacent sequences:  A187144 A187145 A187146 * A187148 A187149 A187150

KEYWORD

sign

AUTHOR

Michael Somos, Mar 05 2011

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 6 09:18 EST 2016. Contains 278775 sequences.