A058754 McKay-Thompson series of class 78A for Monster.

1, 0, 1, 1, 1, 0, 2, 1, 3, 3, 3, 2, 6, 4, 6, 6, 8, 6, 11, 9, 13, 14, 16, 14, 24, 19, 27, 27, 33, 30, 43, 38, 51, 51, 61, 58, 79, 72, 92, 94, 110, 106, 138, 130, 160, 164, 189, 188, 235, 226, 270, 279, 321, 320, 388, 381, 448, 462, 525, 530, 631, 626, 724, 750

Offset

-1,7

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 B + 1 + 1/B, where B = eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/( eta(q^2)*eta(q^3)*eta(q^13)*eta(q^78)), in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(2*Pi*sqrt(2*n/39)) / (2^(3/4) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T78A = 1/q + q + q^2 + q^3 + 2*q^5 + q^6 + 3*q^7 + 3*q^8 + 3*q^9 + 2*q^10 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^6]*eta[q^26]* eta[q^39]/(eta[q^2]*eta[q^3]*eta[q^13]*eta[q^78]);  a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[[[n]], {n, 1, 50}]  (* G. C. Greubel, Jun 30 2018 *)

Prog

(PARI) q='q+O('q^50); B = eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/(q*eta(q^2) *eta(q^3)*eta(q^13)*eta(q^78)); Vec(B + 1 + 1/B) \\ G. C. Greubel, Jun 30 2018

Crossrefs

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

Sequence in context: A366627 A325495 A048865 * A279909 A125087 A271373

Adjacent sequences: A058751 A058752 A058753 * A058755 A058756 A058757

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved