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A112204 McKay-Thompson series of class 63a for the Monster group. 2
1, 0, 2, 2, 1, 2, 3, 2, 4, 6, 6, 6, 9, 8, 13, 14, 15, 18, 23, 22, 29, 34, 35, 44, 52, 52, 65, 74, 80, 92, 110, 114, 134, 152, 164, 188, 215, 230, 266, 296, 321, 362, 412, 438, 503, 558, 602, 674, 755, 810, 912, 1010, 1093, 1210, 1346, 1446, 1614, 1772, 1922, 2118 (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

a(n) ~ exp(4*Pi*sqrt(n)/(3*sqrt(7))) / (sqrt(6) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018

Expansion of (q*T21A)^(1/3), where T21A = A058563. - G. C. Greubel, Jun 20 2018

Expansion of q^(1/2)*(((eta(q^3)*eta(q^7))^2 - (eta(q)*eta(q^21))^2)/( eta(q)*eta(q^3)*eta(q^7)*eta(q^21)))^(2/3) in powers of q. - G. C. Greubel, Jun 20 2018

EXAMPLE

T63a = 1/q + 2*q^5 + 2*q^8 + q^11 + 2*q^14 + 3*q^17 + 2*q^20 + 4*q^23 + ...

MATHEMATICA

CoefficientList[Series[((QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]))^(2/3), {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 120; e21B := eta[q]*eta[q^3]/( eta[q^7]*eta[q^21]); T21A := 1 + e21B + 7/e21B; a:= CoefficientList[ Series[(q*T21A + O[q]^nmax)^(1/3), {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)

PROG

(PARI) q='q+O('q^50); Vec((((eta(q^3)*eta(q^7))^2 - q*(eta(q)*eta(q^21) )^2)/(eta(q)*eta(q^3)*eta(q^7)*eta(q^21)))^(2/3)) \\ G. C. Greubel, Jun 20 2018

CROSSREFS

Sequence in context: A029251 A263073 A133091 * A129710 A298857 A070680

Adjacent sequences:  A112201 A112202 A112203 * A112205 A112206 A112207

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 19 18:16 EST 2019. Contains 319309 sequences. (Running on oeis4.)