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A007263
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Coefficients of completely replicable function "6d".
(Formerly M4995)
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5
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1, 0, 16, -8, 0, 128, 28, 0, 576, -64, 0, 2048, 134, 0, 6304, -288, 0, 17408, 568, 0, 44416, -1024, 0, 106496, 1809, 0, 242480, -3152, 0, 528896, 5316, 0, 1112128, -8704, 0, 2265088, 13990, 0, 4486112
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OFFSET
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-1,3
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COMMENTS
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Original name was "McKay-Thompson series of class 6d for Monster" but this series is non-monstrous. Refer to table in Alexander, et. al. 1990. - Michael Somos, Nov 20 2019
G.f. is a period 1 Fourier series which satisfies f(-1 / (18 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Nov 20 2019
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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D. Alexander, C. Cummins, J. McKay and C. Simons, Completely Replicable Functions, in Groups, Combinatorics & Geometry, (Durham, 1990), pp. 87--98, London Math. Soc. Monograph No. 165.
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FORMULA
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Expansion of (eta(q^3)/eta(q^6))^8 + 16*(eta(q^6)/eta(q^3))^8 in powers of q. - G. A. Edgar, Mar 10 2017
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EXAMPLE
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T6d = 1/q + 16*q - 8*q^2 + 128*q^4 + 28*q^5 + 576*q^7 - 64*q^8 + ...
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MATHEMATICA
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eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[(eta[q^3]/ eta[q^6])^8 + 16*(eta[q^6]/eta[q^3])^8, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 25 2018 *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^3 + A) / eta(x^6 + A))^8; polcoeff( A + 16*x^2/A, n))}; /* Michael Somos, Nov 20 2019 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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