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A134783
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McKay-Thompson series of class 15A for the Monster group with a(0) = 1.
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1
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1, 1, 8, 22, 42, 70, 155, 246, 421, 722, 1101, 1730, 2761, 4062, 6106, 9040, 13065, 18806, 27081, 37950, 53183, 74290, 102213, 140048, 191612, 258426, 348300, 467484, 622023, 825016, 1090957, 1432290, 1875930, 2448610, 3179136, 4114996
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,3
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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 (15)(5)(3)(1).
G.f. is Fourier series of a level 15 modular function. f(-1/ (15 t)) = f(t) where q = exp(2 pi i t).
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EXAMPLE
| 1/q + 1 + 8*q + 22*q^2 + 42*q^3 + 70*q^4 + 155*q^5 + 246*q^6 + 421*q^7 + ...
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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^5 + A) / ( eta(x^3 + A) * eta(x^15 + A) ))^2 / x; polcoeff( (3 + A + 9 / A), n))}
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CROSSREFS
| A058498(n) = a(n) unless n=0. Convolution with A030184 is A028998.
Sequence in context: A030999 A113744 A058508 * A069099 A172473 A145067
Adjacent sequences: A134780 A134781 A134782 * A134784 A134785 A134786
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Nov 22 2007
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