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A058674 McKay-Thompson series of class 42D for Monster. 1
1, 0, 1, 3, 3, 4, 7, 7, 9, 15, 16, 20, 29, 32, 40, 55, 61, 74, 99, 111, 134, 170, 192, 230, 285, 323, 382, 466, 530, 622, 746, 848, 988, 1173, 1331, 1540, 1810, 2052, 2363, 2752, 3114, 3568, 4129, 4663, 5318, 6118, 6895, 7834, 8963, 10078, 11410, 12993, 14579 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -1 + eta(q^2)*eta(q^6)*eta(q^7)*eta(q^21)/(eta(q)*eta(q^3) *eta(q^14)*eta(q^42)) in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T42D = 1/q + q + 3*q^2 + 3*q^3 + 4*q^4 + 7*q^5 + 7*q^6 + 9*q^7 + 15*q^8 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := ((eta[q^2]*eta[q^6]*eta[q^7] *eta[q^21])/(eta[q]*eta[q^3]*eta[q^14]*eta[q^42])); a:=CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

PROG

(PARI) q='q+O('q^50); A = -1 + eta(q^2)*eta(q^6)*eta(q^7)*eta(q^21)/( eta(q)*eta(q^3)*eta(q^14)*eta(q^42))/q; Vec(A) \\ G. C. Greubel, Jun 24 2018

CROSSREFS

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

Sequence in context: A007448 A155689 A051263 * A152651 A091973 A327726

Adjacent sequences:  A058671 A058672 A058673 * A058675 A058676 A058677

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)