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A058732 McKay-Thompson series of class 60b for Monster. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)