A058557 - OEIS

A058557

McKay-Thompson series of class 20b for Monster.

1, 4, 3, 16, 20, 48, 55, 108, 141, 248, 326, 516, 662, 1048, 1335, 2000, 2547, 3672, 4689, 6588, 8379, 11500, 14513, 19644, 24688, 32896, 41115, 53964, 67301, 87312, 108385, 139124, 171876, 218852, 269284, 339996, 416665, 522104, 637698, 793704, 965989, 1194888, 1448933, 1782800

(list; graph; refs; listen; history; text; internal format)

OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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 + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3, in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T20b = 1/q + 4*q + 3*q^3 + 16*q^5 + 20*q^7 + 48*q^9 + 55*q^11 + 108*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^3; a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3; Vec(A + q/A) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A092398 A288199 A127675 * A287978 A288368 A288595

Adjacent sequences: A058554 A058555 A058556 * A058558 A058559 A058560

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

STATUS

approved