A058732 - OEIS

A058732

McKay-Thompson series of class 60b for Monster.

1, 0, 2, 1, 1, 3, 5, 2, 5, 3, 7, 7, 12, 8, 15, 15, 18, 20, 29, 23, 38, 36, 47, 48, 64, 61, 85, 83, 101, 107, 141, 132, 177, 177, 212, 230, 282, 277, 350, 355, 426, 450, 546, 545, 665, 695, 807, 857, 1009, 1028, 1236, 1287, 1479, 1570, 1820, 1888, 2205, 2314

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OFFSET

-1,3

REFERENCES

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = -1..1000

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/15)) / (2*15^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of A - q/A, where q^(1/2)*(eta(q^2)*eta(q^3)*eta(q^10) *eta(q^15)/(eta(q)*eta(q^5)*eta(q^6)*eta(q^30))), in powers of q. - G. C. Greubel, Jun 16 2018

EXAMPLE

T60b = 1/q + 2*q^3 + q^5 + q^7 + 3*q^9 + 5*q^11 + 2*q^13 + 5*q^15 + 3*q^17 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^3]* eta[q^10]*eta[q^15]/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q) *eta(q^5)*eta(q^6)*eta(q^30))); Vec(A - q/A) \\ G. C. Greubel, Jun 16 2018

CROSSREFS

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

Sequence in context: A275866 A007754 A144866 * A060082 A102225 A183262

Adjacent sequences: A058729 A058730 A058731 * A058733 A058734 A058735

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Vaclav Kotesovec, Sep 07 2017

STATUS

approved