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A091406
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Reversion of series for j-function.
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4
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1, 744, 750420, 872769632, 1102652742882, 1470561136292880, 2037518752496883080, 2904264865530359889600, 4231393254051181981976079, 6273346050902229242859370584, 9433668720359866477436486024652
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OFFSET
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1,2
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COMMENTS
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Invert j = 1/q + 744 + 196884*q + 21493760 + ... to get q = 1/j + 744/j^2 + 750420/j^2 + ...
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REFERENCES
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J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, see p. 482.
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LINKS
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Table of n, a(n) for n=1..11.
Y.-H. He and V. Jejjala, Modular Matrix Models.
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MAPLE
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(It would be nice to have a Maple program for this sequence.
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MATHEMATICA
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max = 9; s1 = 1728*Series[ KleinInvariantJ[t], {t, 0, 2*max} ] /. t -> -2*I*(Pi/Log[q]); s2 = InverseSeries[ Series[ s1, {q, 0, max} ], j] /. j -> 1/x; Rest[ CoefficientList[ s2, x ] ](* From Jean-François Alcover, Feb 16 2012 *)
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PROG
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(PARI) {a(n) = local(A); if( n<1, 0, A = O(x^n); A = x * (eta(x^2 + A) / eta(x + A))^24; polcoeff( serreverse( A / (1 + 256*A)^3), n))} /* Michael Somos, Jul 13 2004 */
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CROSSREFS
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Cf. A000521, A178451. See A066396 for another version.
Sequence in context: A178451 A066395 A161557 * A066396 A099819 A051978
Adjacent sequences: A091403 A091404 A091405 * A091407 A091408 A091409
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Mar 03 2004
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STATUS
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approved
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