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COMMENTS
| "The most natural normalization [of the j function] is to set the constant term equal to 24, the number given by Rademacher's infinite series for coefficients of the j function". [Borcherds]
Changing the term 744 to 24 gives A007240, the McKay-Thompson series of class 1A for Monster simple group.
sigma_3(n) is the sum of the cubes of the divisors of n (A001158).
Klein's absolute invariant J=j/1728 is Gamma-modular.
(n+1)*A000521(n)/24 yields integral values - see A161395 [From Alexander R. Povolotsky (pevnev(AT)juno.com), Jun 09 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 07 2009: (Start)
Equals convolution square of A161361: (1, 372, 29250, -134120, 54261375,...)
and row sums of triangle A161362. (End)
This sequence is mentioned in the Bruinier-Ono paper in which also appears the finite algebraic formula for the partition function. See chapter 4.1: Singular moduli for j(z). - Omar E. Pol, Nov 03 2011
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REFERENCES
| R. E. Borcherds, Review of "Moonshine Beyond the Monster ..." (Cambridge, 2006), Bull. Amer. Math. Soc., 45 (2008), 675-679.
J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 115.
H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1996, pp. 376ff.
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc., 42 (2005), 137-162.
A. Erdelyi, Higher Transcendental Functions, McGraw-Hill, 1955, Vol. 3, p. 20.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
T. Gannon, Postcards from the edge, or Snapshots of the theory of generalised Moonshine, arXiv:math/0109067.
M. Kaneko, The Fourier coefficients and the singular moduli of the elliptic modular function j(tau), Memoirs Faculty Engin. Sci., Kyoto Inst. Technology, 44 (March 1996), pp. 1-5.
M. Kaneko, Fourier coefficients of the elliptic modular function j(tau) (in Japanese), Rokko Lectures in Mathematics 10, Dept. Math., Faculty of Science, Kobe University, Rokko, Kobe, Japan, 2001.
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998.
S. Lang, Introduction to Modular Forms, Springer-Verlag, 1976, p. 12.
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.
B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 56.
J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, see p. 482.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. G. Thompson, Some numerology between the Fischer-Griess Monster and the elliptic modular function, Bull. London Math. Soc., 11 (1979), 352-353.
A. van Wijngaarden, On the coefficients of the modular invariant J(tau), Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, 56 (1953), 389-400 [ gives 100 terms ].
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