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A107080
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McKay-Thompson series of class 4A for the Monster group.
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8
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1, 0, 276, 2048, 11202, 49152, 184024, 614400, 1881471, 5373952, 14478180, 37122048, 91231550, 216072192, 495248952, 1102430208, 2390434947, 5061476352, 10487167336, 21301241856, 42481784514, 83300614144, 160791890304, 305854488576, 573872089212, 1063005978624, 1945403602764, 3519965179904
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OFFSET
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-1,3
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COMMENTS
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Also character of extremal vertex operator algebra of rank 12.
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LINKS
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G. Hoehn (gerald(AT)math.ksu.edu), Selbstduale Vertexoperatorsuperalgebren und das Babymonster, Doctoral Dissertation, Univ. Bonn, Jul 15 1995 (pdf, ps).
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FORMULA
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G.f.: (1/x)(Product_{k>0} (1+x^k)/(1+x^(2k)))^24 -24.
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EXAMPLE
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T4A = 1/q + 276q + 2048q^2 + 11202q^3 + 49152q^4 + 184024q^5 +...
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MATHEMATICA
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a[0] = 0; a[n_] := SeriesCoefficient[ Product[1 - q^k, {k, 1, n+1, 2}]^24/q, {q, 0, n}] // Abs; Table[a[n], {n, -1, 20}] (* Jean-François Alcover, Oct 14 2013, after Michael Somos *)
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PROG
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(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 / (eta(x + A) * eta(x^4 + A)))^24 - 24*x, n))};
(PARI) q='q+O('q^66); Vec(+40*q+(eta(q)^4 / eta(q^4)^4 - q*4^2*eta(q^4)^4 / eta(q)^4)^2) \\ Joerg Arndt, Mar 23 2017
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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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