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A058533 McKay-Thompson series of class 18C for the Monster group. 5
1, 0, 3, -2, 3, -6, 10, -12, 15, -22, 30, -36, 44, -60, 78, -96, 117, -150, 190, -228, 276, -340, 420, -504, 603, -732, 885, -1052, 1245, -1488, 1770, -2088, 2454, -2902, 3420, -3996, 4666, -5460, 6378, -7400, 8583, -9972, 11566, -13344, 15378, -17752, 20448 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

A058533, A123676, A215412, A058644, A215413 are all essentially the same sequence. - N. J. A. Sloane, Aug 09 2012

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 = -1..5000

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

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -1 + psi(q) / (q * psi(q^9)) + 3 * q * psi(q^9) / psi(q) in powers of q where psi() is a Ramanujan theta function. - Michael Somos, Aug 09 2012

a(n) = A123676(n) = A215412(n) = A215413(n) unless n=0. a(n) = -(-1)^n * A058644(n). - Michael Somos, Aug 09 2012

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

EXAMPLE

T18C = 1/q + 3*q - 2*q^2 + 3*q^3 - 6*q^4 + 10*q^5 - 12*q^6 + 15*q^7 - ...

MATHEMATICA

QP = QPochhammer; s = -q + QP[q^3]^6 / (QP[q]*QP[q^2]*QP[q^6]^2*QP[q^9]* QP[q^18]) + O[q]^50; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 12 2015, adapted from PARI *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( -x + eta(x^3 + A)^6 / (eta(x + A) * eta(x^2 + A) * eta(x^6 + A)^2 * eta(x^9 + A) * eta(x^18 + A)), n))}; /* Michael Somos, Aug 09 2012 */

CROSSREFS

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

Cf. A123676, A215412, A215413.

Sequence in context: A187501 A274462 A050062 * A215413 A058644 A049923

Adjacent sequences:  A058530 A058531 A058532 * A058534 A058535 A058536

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified October 17 15:01 EDT 2019. Contains 328116 sequences. (Running on oeis4.)