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A007266
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McKay-Thompson series of class 9A for Monster.
(Formerly M5192)
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3
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1, 0, 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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-1,3
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COMMENTS
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G.f. A(x) satisfies 0=f(A(x)+6,A(x^2)+6) where f(u,v)=(u+v)^3+uv(27+9(u+v)-uv). - Michael Somos, Jun 16 2004
Expansion of eta(q^3)^12/(eta(q)eta(q^9))^6-6 in powers of q.
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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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FORMULA
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EXAMPLE
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T9A = 1/q + 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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QP = QPochhammer; s = QP[q^3]^12/(QP[q]*QP[q^9])^6 - 6*q + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, adapted from PARI *)
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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))^6-6*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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