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A134786
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McKay-Thompson series of class 4A for the Monster group with a(0) = 4.
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7
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1, 4, 276, 2048, 11202, 49152, 184024, 614400, 1881471, 5373952, 14478180, 37122048, 91231550, 216072192, 495248952, 1102430208, 2390434947, 5061476352, 10487167336, 21301241856, 42481784514, 83300614144, 160791890304
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,2
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REFERENCES
| M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
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LINKS
| Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| Associated with permutations in Mathieu group M24 of shape (4)^4(2)^2(1)^4.
G.f. is Fourier series of a level 4 modular function. f(-1/ (4 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
| 1/q + 4 + 276*q + 2048*q^2 + 11202*q^3 + 49152*q^4 + 184024*q^5 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); A = ( eta(x + A) / eta(x^4 + A) )^8 / x; polcoeff( 12 + A + 256 / A, n))}
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CROSSREFS
| A107080(n) = a(n) unless n=0. Convolution with A030212 is A037219.
Cf. A097340. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
A134786, A045479, A007191, A097340, A035099, A007246, A107080 are all essentially the same sequence.
Sequence in context: A108134 A000320 A101758 * A190635 A202031 A074309
Adjacent sequences: A134783 A134784 A134785 * A134787 A134788 A134789
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Nov 22 2007
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