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A007241
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McKay-Thompson series of class 2A for Monster.
(Formerly M5176)
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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; refs; listen; history; internal format)
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OFFSET
| -1,2
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REFERENCES
| 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.
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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=-1..1000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
Index entries for McKay-Thompson series for Monster simple group
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FORMULA
| 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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PROG
| (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
| Cf. A007267, A045478.
A045478, A007241, A106207, A007267, A101558 are all essentially the same sequence.
Sequence in context: A159399 A184687 * A106207 A100089 A151598 A003787
Adjacent sequences: A007238 A007239 A007240 * A007242 A007243 A007244
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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