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A112178 McKay-Thompson series of class 36i for the Monster group. 3
1, -1, 0, -1, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, -1, 0, 2, -1, 0, -2, -2, 0, 0, -1, 0, 2, -1, 0, -2, -1, 0, -1, -2, 0, 4, -3, 0, -4, -3, 0, 0, -3, 0, 5, -2, 0, -4, -2, 0, -2, -3, 0, 8, -5, 0, -7, -6, 0, -1, -5, 0, 9, -4, 0, -8, -4, 0, -3, -6, 0, 14, -9, 0, -13, -10, 0, -2, -9, 0, 16, -8, 0, -14, -8, 0, -5, -11, 0, 24, -14, 0, -21, -16, 0, -3 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,19
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A - q/A, where A = q^(1/2)*(eta(q^3)*eta(q^18)^2* eta(q^27)/(eta(q^6)*eta(q^9)^2*eta(q^54))), in powers of q. - G. C. Greubel, Jun 16 2018
EXAMPLE
T36i = 1/q -q -q^5 -q^7 -q^13 +q^17 -q^23 -q^29 -q^31 +2*q^35 +...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^18]^2* eta[q^27]/(eta[q^6]*eta[q^9]^2*eta[q^54])); a:=CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^18)^2* eta(q^27)/(eta(q^6) *eta(q^9)^2*eta(q^54))); Vec(A - q/A) \\ G. C. Greubel, Jun 16 2018
CROSSREFS
Sequence in context: A356262 A281228 A284575 * A134663 A000925 A258279
KEYWORD
sign
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved

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Last modified March 19 06:29 EDT 2024. Contains 370953 sequences. (Running on oeis4.)