A058626 McKay-Thompson series of class 30e for Monster.

1, 0, -1, 2, 1, 0, 0, -2, 2, 0, 2, 0, 0, 4, 3, 2, 0, -4, 5, 2, 6, 0, -5, 8, 3, 4, 0, -6, 10, 4, 11, 0, -10, 20, 9, 8, 0, -16, 21, 6, 19, 0, -15, 34, 16, 20, 0, -28, 43, 16, 35, 0, -33, 60, 25, 34, 0, -44, 71, 28, 62, 0, -60, 110, 47, 60, 0, -84, 126, 44, 99, 0, -89, 176, 79, 108, 0, -136

Offset

-1,4

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 (2 + T15b(q) + T15b(q^2) + T15b(q)*T15b(q^2))/(5 + T15b(q) + T15b(q^2)), where T15b = A058513 and T15b(q^2) = T15b(q -> q^2), in powers of q. - G. C. Greubel, Jun 23 2018

Example

T30e = 1/q - q + 2*q^2 + q^3 - 2*q^6 + 2*q^7 + 2*q^9 + 4*q^12 + 3*q^13 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; B1:= (eta[q]/eta[q^25]); D1:= q*(eta[q^3]/eta[q^15])^2; C1:= (eta[q^3]*eta[q^5]/(eta[q]*eta[q^15]))^3; T25A := B1 + 5/B1; A := (eta[q^3]/eta[q^75]); T15b := 2 + (-5 + T25A*(A + 5/A))*(-B1 + A)*(1/(A*B1))^2*(D1^3/C1)/q^3; a:= CoefficientList[ Series[q*(2 + T15b + (T15b /. {q -> q^2}) + T15b*(T15b /. {q -> q^2}) )/(5 + T15b + (T15b /. {q -> q^2})), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

Crossrefs

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

Sequence in context: A103344 A123484 A008626 * A258278 A122856 A328797

Adjacent sequences: A058623 A058624 A058625 * A058627 A058628 A058629

Keyword

sign,changed

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(24) onward added by G. C. Greubel, Jun 23 2018

Status

approved