A112170 McKay-Thompson series of class 30f for the Monster group.

1, 1, 1, 0, -2, 2, 0, 1, 0, -1, 2, 1, 3, 0, -2, 5, 2, 3, 0, -5, 7, 3, 4, 0, -5, 9, 3, 7, 0, -7, 14, 8, 11, 0, -14, 21, 7, 13, 0, -14, 26, 11, 20, 0, -21, 39, 16, 26, 0, -32, 51, 20, 34, 0, -38, 65, 25, 47, 0, -49, 90, 40, 63, 0, -74, 118, 44, 77, 0, -85, 146, 60, 105, 0, -111, 196, 80, 132, 0, -152

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..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 sqrt(2 + T15b), in powers of q, where T15b = A058513. - G. C. Greubel, Jun 30 2018

Example

T30f = 1/q + q + q^3 - 2*q^7 + 2*q^9 + q^13 - q^17 + 2*q^19 + q^21 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]);
d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= 2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3; a:= CoefficientList[ Series[(q*(T15b + 2) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jun 30 2018, fixed by Vaclav Kotesovec, Jul 03 2018 *)

Crossrefs

Sequence in context: A317675 A332902 A204423 * A366475 A259976 A113685

Adjacent sequences: A112167 A112168 A112169 * A112171 A112172 A112173

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved