A058755 McKay-Thompson series of class 78B for Monster.

1, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 2, -1, 0, 0, 1, -2, 2, -2, 1, 0, 1, -3, 4, -3, 2, -1, 2, -4, 5, -5, 3, -2, 3, -6, 8, -7, 4, -2, 5, -9, 11, -10, 6, -4, 6, -12, 16, -14, 8, -6, 11, -17, 21, -19, 13, -10, 14, -24, 30, -26, 17, -14, 21, -31, 38, -35, 25, -20, 26, -42, 52, -46, 33, -28, 38, -56, 68, -62, 47, -38, 49, -75

Offset

-1,13

Comments

Also McKay-Thompson series of class 78C for Monster. - Michel Marcus, Feb 19 2014

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).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of 1 + 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 19 2018

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/39)) / (2 * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T78B = 1/q - q^4 + q^5 - q^6 + q^7 - q^10 + 2*q^11 - q^12 + q^15 - 2*q^16 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= 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[q*(1 + A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^50); A = 1 + eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/( eta(q^2)*eta(q^3)*eta(q^13)*eta(q^78))/q; Vec(A) \\ G. C. Greubel, Jun 19 2018

Crossrefs

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

Cf. A128519 (same sequence except for n=0).

Sequence in context: A261684 A048571 A025880 * A128519 A303979 A301573

Adjacent sequences: A058752 A058753 A058754 * A058756 A058757 A058758

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved