A058671 McKay-Thompson series of class 42A for Monster.

1, 0, 2, 2, 3, 2, 9, 6, 11, 14, 18, 16, 31, 30, 46, 50, 66, 66, 106, 102, 146, 160, 204, 216, 297, 306, 401, 448, 552, 594, 777, 816, 1023, 1134, 1377, 1492, 1858, 1998, 2427, 2684, 3183, 3488, 4219, 4566, 5429, 6000, 7020, 7688, 9115, 9918, 11593, 12806

Offset

-1,3

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 A + 2 + 1/A, where A = ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21) )/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2, 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

T42A = 1/q + 2*q + 2*q^2 + 3*q^3 + 2*q^4 + 9*q^5 + 6*q^6 + 11*q^7 + 14*q^8 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A := ((eta[q]*eta[q^6]*eta[q^14]* eta[q^21])/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42]))^2; a := CoefficientList[Series[2 + A + 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 = ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21))/( eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2/q; Vec(A + 2 + 1/A) \\ G. C. Greubel, Jun 24 2018

Crossrefs

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

Sequence in context: A016012 A069138 A179592 * A016002 A098189 A162733

Adjacent sequences: A058668 A058669 A058670 * A058672 A058673 A058674

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved