A058674 McKay-Thompson series of class 42D for Monster.

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

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 * A349252 A152651 A343396

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