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A112180 McKay-Thompson series of class 40a for the Monster group. 1
1, 0, 3, 4, 4, 4, 7, 12, 13, 16, 22, 28, 38, 44, 55, 72, 83, 104, 129, 156, 187, 220, 273, 328, 384, 452, 539, 652, 757, 880, 1041, 1220, 1428, 1652, 1924, 2244, 2585, 2992, 3458, 3992, 4581, 5244, 6053, 6936, 7910, 9024, 10303, 11784, 13380, 15176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 A - q/A, where A = q^(1/2)*(eta(q^4)*eta(q^5)/( eta(q)* eta(q^20))), in powers of q. - G. C. Greubel, Jun 26 2018

a(n) ~ exp(Pi*sqrt(2*n/5)) / (2^(5/4) * 5^(1/4) *  n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T40a = 1/q +3*q^3 +4*q^5 +4*q^7 +4*q^9 +7*q^11 +12*q^13 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^5]/( eta[q]*eta[q^20])); a := CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)); Vec(A - q/A) \\ G. C. Greubel, Jun 26 2018

CROSSREFS

Sequence in context: A259884 A283972 A213509 * A058559 A232092 A185271

Adjacent sequences:  A112177 A112178 A112179 * A112181 A112182 A112183

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)