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A045491
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McKay-Thompson series of class 9A for the Monster group with a(0) = 3.
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3
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1, 3, 27, 86, 243, 594, 1370, 2916, 5967, 11586, 21870, 39852, 71052, 123444, 210654, 352480, 581013, 942786, 1510254, 2388204, 3734964, 5777788, 8852004, 13434984, 20218395, 30177684, 44704413, 65743348, 96033357, 139368816
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OFFSET
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-1,2
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COMMENTS
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Given g.f. A(x), B(q) = 3 + A(q) satisfies 0 = f(B(q), B(q^2)) where f(u, v) = (u + v)^3 + u*v*(27 + 9*(u + v) - u*v). - Michael Somos, Jun 16 2004
Expansion of eta(q^3)^12 / (eta(q) * eta(q^9))^6 - 3 in powers of q.
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LINKS
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FORMULA
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EXAMPLE
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G.f. = 1/q + 3 + 27*q + 86*q^2 + 243*q^3 + 594*q^4 + 1370*q^5 + 2916*q^6 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ -3 + (1/q) (QPochhammer[ q^3]^2 / (QPochhammer[ q] QPochhammer[ q^9]))^6, {q, 0, n}]; (* Michael Somos, Feb 22 2015 *)
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PROG
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(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^3 + A)^12 / (eta(x + A) * eta(x^9 + A))^6 - 3*x, n))}; /* Michael Somos, Jun 16 2004 */
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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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