A058714 McKay-Thompson series of class 56A for the Monster group.

1, 0, 1, 2, 1, 2, 3, 4, 5, 6, 8, 8, 10, 12, 15, 18, 22, 26, 29, 34, 39, 48, 55, 64, 76, 84, 97, 112, 128, 146, 168, 192, 217, 246, 277, 316, 355, 402, 454, 508, 572, 640, 721, 804, 898, 1008, 1119, 1248, 1392, 1548, 1718, 1910, 2118, 2344, 2598, 2872, 3181

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^4)*eta(q^14)*eta(q^28)/(eta(q)*eta(q^7) *eta(q^8)*eta(q^56)) in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T56A = 1/q + q + 2*q^2 + q^3 + 2*q^4 + 3*q^5 + 4*q^6 + 5*q^7 + 6*q^8 + 8*q^9 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q^2]*eta[q^4]*eta[q^14]* eta[q^28]/(eta[q]*eta[q^7]*eta[q^8]*eta[q^56])); a:= CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}]  (* G. C. Greubel, Jun 27 2018 *)

Prog

(PARI) q='q+O('q^50); Vec(-1 + eta(q^2)*eta(q^4)*eta(q^14)*eta(q^28)/(q* eta(q)*eta(q^7)*eta(q^8)*eta(q^56))) \\ G. C. Greubel, Jun 27 2018

Crossrefs

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

Sequence in context: A137846 A080915 A239484 * A057045 A237753 A058700

Adjacent sequences: A058711 A058712 A058713 * A058715 A058716 A058717

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved