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Search: id:A106207
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| A106207 |
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Expansion of 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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+0
1
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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.
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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EXAMPLE
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1/q -24 +4372q +96256q^2 +1240002q^3 +...
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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^2*4096/A, n))}
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CROSSREFS
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Cf. A007241 is unsigned version.
Sequence in context: A166768 A159399 A007241 this_sequence A100089 A151598 A003787
Adjacent sequences: A106204 A106205 A106206 this_sequence A106208 A106209 A106210
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 25 2005
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