A058619 McKay-Thompson series of class 30a for Monster.

1, -4, -4, -5, -7, -13, -15, -24, -35, -41, -63, -89, -102, -150, -187, -235, -318, -402, -485, -635, -788, -972, -1221, -1520, -1810, -2281, -2787, -3343, -4105, -4967, -5911, -7232, -8639, -10275, -12334, -14724, -17378, -20757, -24550, -28849, -34174, -40294, -47060, -55485, -64881

Offset

-1,2

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of A - 3*q/A, where A= q^(1/2)*eta(q)*eta(q^5)/(eta(q^3) * eta(q^15)), in powers of q. - G. C. Greubel, Jun 23 2018

a(n) ~ -exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T30a = 1/q - 4*q - 4*q^3 - 5*q^5 - 7*q^7 - 13*q^9 - 15*q^11 - 24*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q]*eta[q^5]/( eta[q^3]*eta[q^15])); a:= CoefficientList[Series[A - 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

Prog

(PARI) q='q+O('q^50); A= eta(q)*eta(q^5)/(eta(q^3)*eta(q^15)); Vec(A - 3*q/A) \\ G. C. Greubel, Jun 23 2018

Crossrefs

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

Sequence in context: A103483 A170934 A079999 * A198999 A095945 A072231

Adjacent sequences: A058616 A058617 A058618 * A058620 A058621 A058622

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 23 2018

Status

approved