A052240 McKay-Thompson series of class 7B for the Monster group.

1, 0, 2, 8, -5, -4, -10, 12, -7, 8, 46, -36, -26, -44, 46, -28, 42, 188, -132, -96, -167, 172, -98, 120, 596, -420, -286, -492, 496, -280, 368, 1680, -1151, -792, -1332, 1320, -735, 916, 4264, -2908, -1960, -3252, 3200, -1764, 2230, 10104

Offset

-1,3

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

N. D. Elkies, Elliptic and modular curves over finite fields and related computational issues, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 39.

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

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of (eta(q) / eta(q^7))^4 + 4 in powers of q.

Example

T7B = 1/q + 2*q + 8*q^2 - 5*q^3 - 4*q^4 - 10*q^5 + 12*q^6 - 7*q^7 + 8*q^8 + ...

Mathematica

QP = QPochhammer; s = (QP[q]/QP[q^7])^4 + 4*q + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015 *)

Prog

(PARI) q='q+O('q^30); Vec(4*q + (eta(q)/eta(q^7))^4) \\ G. C. Greubel, May 05 2018

Crossrefs

Essentially same as A030181.

Sequence in context: A021782 A342977 A155808 * A035490 A248936 A019678

Adjacent sequences: A052237 A052238 A052239 * A052241 A052242 A052243

Keyword

sign

Author

N. J. A. Sloane, Nov 25 2000

Status

approved