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Search: id:A134782
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| A134782 |
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McKay-Thompson series of class 14A for the Monster group with a(0) = 1. |
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+0
2
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| 1, 1, 11, 20, 57, 92, 207, 312, 623, 932, 1674, 2464, 4162, 6024, 9595, 13748, 21126, 29820, 44449, 62004, 90191, 124288, 177135, 241632, 338508, 457272, 631031, 845008, 1150752, 1528380, 2057700, 2712192, 3614217, 4730148, 6245541, 8119672
(list; graph; listen)
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OFFSET
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-1,3
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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 (14)(7)(2)(1).
G.f. is Fourier series of a level 14 modular function. f(-1/ (14 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
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1/q + 1 + 11*q + 20*q^2 + 57*q^3 + 92*q^4 + 207*q^5 + 312*q^6 + 623*q^7 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); A = (eta(x + A) * eta(x^7 + A) / ( eta(x^2 + A) * eta(x^14 + A) ))^3 / x; polcoeff( (4 + A + 8 / A), n))}
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CROSSREFS
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A058497(n) = a(n) unless n=0. Convolution with A030187 is A028997.
Sequence in context: A076851 A164576 A058497 this_sequence A067969 A068599 A085187
Adjacent sequences: A134779 A134780 A134781 this_sequence A134783 A134784 A134785
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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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