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A134786
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McKay-Thompson series of class 4A for the Monster group with a(0) = 4.
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7
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1, 4, 276, 2048, 11202, 49152, 184024, 614400, 1881471, 5373952, 14478180, 37122048, 91231550, 216072192, 495248952, 1102430208, 2390434947, 5061476352, 10487167336, 21301241856, 42481784514, 83300614144, 160791890304
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OFFSET
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-1,2
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LINKS
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FORMULA
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Associated with permutations in Mathieu group M24 of shape (4)^4(2)^2(1)^4.
G.f. is a period 1 Fourier series which satisfies f(-1 / (4 t)) = f(t) where q = exp(2 Pi i t).
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EXAMPLE
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G.f. = 1/q + 4 + 276*q + 2048*q^2 + 11202*q^3 + 49152*q^4 + 184024*q^5 + ...
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MATHEMATICA
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a[0] = 4; a[n_] := SeriesCoefficient[ Product[1 - q^k, {k, 1, n+1, 2}]^24/q, {q, 0, n}] // Abs; Table[a[n], {n, -1, 21}] (* Jean-François Alcover, Oct 14 2013, after Michael Somos *)
a[ n_] := SeriesCoefficient[ -20 + QPochhammer[ -q, q^2]^24 / q, {q, 0, n}]; (* Michael Somos, May 05 2016 *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, A = x^2 * O(x^n); A = (eta(x + A) / eta(x^4 + A))^8 / x; polcoeff( 12 + A + 256 / A, n))};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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