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Search: id:A134785
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| A134785 |
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McKay-Thompson series of class 8A for the Monster group with a(0) = 2. |
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1
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| 1, 2, 36, 128, 386, 1024, 2488, 5632, 12031, 24576, 48308, 91904, 170110, 307200, 542872, 941056, 1602819, 2686976, 4439688, 7238272, 11657090, 18561024, 29242240, 45617664, 70507772, 108036096, 164192188, 247620352, 370726652
(list; graph; listen)
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OFFSET
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-1,2
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REFERENCES
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M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
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LINKS
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Index entries for McKay-Thompson series for Monster simple group
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FORMULA
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Associated with permutations in Mathieu group M24 of shape (8)^2(4)(2)(1)^2.
G.f. is Fourier series of a level 8 modular function. f(-1/ (8 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
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q^-1 + 2 + 36*q + 128*q^2 + 386*q^3 + 1024*q^4 + 2488*q^5 + 5632*q^6 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); polcoeff( -6 + ( eta(x^2 + A) * eta(x^4 + A) / eta(x + A) / eta(x^8 + A) )^8 / x, n))}
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CROSSREFS
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A007265(n) = a(n) unless n=0. Convolution with A030207 is A029713.
Cf. A131123, A045490. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
Sequence in context: A081310 A069067 A145450 this_sequence A143745 A007757 A141217
Adjacent sequences: A134782 A134783 A134784 this_sequence A134786 A134787 A134788
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Nov 22 2007
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