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A134784
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McKay-Thompson series of class 11A for the Monster group with a(0) = 2.
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0
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1, 2, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666
(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 (11)^2(1)^2.
G.f. is Fourier series of a level 11 modular function. f(-1/ (11 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
| 1/q + 2 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...
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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^11 + A) / ( eta(x^2 + A) * eta(x^22 + A) ))^2 / x; polcoeff( 3 + (1 + A) * (1 + 16 / A^2), n))}
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CROSSREFS
| A058205(n) = a(n) unless n=0. Convolution with A006571 is A028996.
Cf. A128525, A003295. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 13 2008]
Sequence in context: A165637 A100271 A046973 * A023256 A073775 A141860
Adjacent sequences: A134781 A134782 A134783 * A134785 A134786 A134787
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Nov 22 2007
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