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A112215 McKay-Thompson series of class 90b for the Monster group. 3
1, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, -1, 1, 0, 0, -1, 2, -2, 2, -1, 0, -1, 3, -2, 1, -1, 1, -2, 4, -5, 3, -1, 1, -2, 4, -6, 4, -2, 3, -5, 6, -7, 6, -2, 1, -6, 10, -10, 9, -6, 4, -7, 12, -12, 9, -7, 6, -10, 18, -20, 13, -8, 9, -12, 18, -24, 20, -12, 13, -21, 27, -29, 24, -14, 13, -25, 36, -38, 35, -25, 19, -30, 46, -46, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,19

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q^(1/3)*(eta(q)*eta(q^6)*eta(q^10)*eta(q^15))/(eta(q^2) *eta(q^3)*eta(q^5)*eta(q^30)) in powers of q. - G. C. Greubel, Jun 06 2018

a(n) ~ (-1)^n * exp(2*Pi*sqrt(n/5)/3) / (2 * sqrt(3) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T90b = 1/q - q^2 - q^20 + q^23 - q^32 + q^35 - q^38 + q^41 - q^50 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/3)* (eta[q]*eta[q^6]*eta[q^10]*eta[q^15])/(eta[q^2]*eta[q^3]*eta[q^5]* eta[q^30]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 04 2018 *)

nmax = 100; CoefficientList[Series[Product[(1 - x^(2*k - 1))*(1 - x^(30*k - 15))/((1 - x^(6*k - 3))*(1 - x^(10*k - 5))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 29 2018 *)

PROG

(PARI) q='q+O('q^80); F=(eta(q)*eta(q^6)*eta(q^10)*eta(q^15))/(eta(q^2) *eta(q^3)*eta(q^5)*eta(q^30)); Vec(F) \\ G. C. Greubel, Jun 06 2018

CROSSREFS

Sequence in context: A307012 A112211 A246575 * A176389 A076451 A230536

Adjacent sequences:  A112212 A112213 A112214 * A112216 A112217 A112218

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified October 23 19:37 EDT 2019. Contains 328373 sequences. (Running on oeis4.)