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Search: id:A007241
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| A007241 |
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McKay-Thompson series of class 2A for Monster.
(Formerly M5176)
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+0
200
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| 1, 24, 4372, 96256, 1240002, 10698752, 74428120, 431529984, 2206741887, 10117578752, 42616961892, 166564106240, 611800208702, 2125795885056, 7040425608760, 22327393665024, 68134255043715, 200740384538624
(list; graph; listen)
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OFFSET
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-1,2
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REFERENCES
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J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 195.
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
S. Ramanujan, Modular Equations and Approximations to pi, pp. 23-39 of Collected Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., AMS Chelsea 2000. See page 26.
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LINKS
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T. D. Noe, Table of n, a(n) for n=-1..1000
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FORMULA
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G.f. 48+64(g_n^(24)+g_n^(-24)) where q=e^(-pi sqrt(n)) and g_n is Ramanujan's class invariant.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<-1, 0, n++; A=prod(k=1, (n+1)\2, 1-x^(2*k-1), 1+x*O(x^n))^24; polcoeff( A+x*48+x^2*4096/A, n))}
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CROSSREFS
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Cf. A007267, A045478.
Sequence in context: A072529 A071639 A061530 this_sequence A106207 A100089 A003787
Adjacent sequences: A007238 A007239 A007240 this_sequence A007242 A007243 A007244
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KEYWORD
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nonn,nice
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AUTHOR
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njas
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