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A058536
McKay-Thompson series of class 18a for Monster.
1
1, 0, 1, 4, 0, -4, 10, 0, 6, 20, 0, -4, 35, 0, 1, 60, 0, -4, 100, 0, 16, 164, 0, -28, 261, 0, 32, 400, 0, -28, 600, 0, 22, 884, 0, -32, 1291, 0, 68, 1864, 0, -116, 2656, 0, 140, 3740, 0, -120, 5205, 0, 100, 7184, 0, -144, 9842, 0, 262, 13388, 0, -392, 18082, 0, 449, 24244, 0, -420, 32300
OFFSET
-1,4
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^2/A, where q*(eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18) ))^4, in powers of q. - G. C. Greubel, Jun 20 2018
EXAMPLE
T18a = 1/q + q + 4*q^2 - 4*q^4 + 10*q^5 + 6*q^7 + 20*q^8 - 4*q^10 + 35*q^11 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A := q*(eta[q^6]*eta[q^9]/(eta[q^3]* eta[q^18]))^4; a:= CoefficientList[Series[A + q^2/A, {q, 0, 80}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 20 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^4; Vec(A + q^2/A) \\ G. C. Greubel, Jun 20 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(24) onward added by G. C. Greubel, Jun 20 2018
STATUS
approved