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REFERENCES
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J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 115.
H. Cohen, Course in Computational Number Theory, page 379.
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).
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.
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.
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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PROGRAM
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(PARI) a(n)=local(A); if(n<-1, 0, A=x^(2*n+2)*O(x); A=x*(eta(x+A)*eta(x^4+A)^2/eta(x^2+A)^3)^8; polcoeff(subst(256*(1-x+x^2)^3/(x-x^2)^2, x, 16*A), 2*n))
(PARI) a(n)=local(A); if(n<-1, 0, A=x^(5*n+5)*O(x); A=(eta(x+A)/eta(x^5+A))^6/x; polcoeff(subst( (x^2+10*x+5)^3/x, x, A), 5*n)) /* Michael Somos Apr 30 2004 */
(PARI) a(n)=local(A); if(n<-1, 0, A=x^2*O(x^n); A=x*(eta(x^2+A)/eta(x+A))^24; polcoeff((1+256*A)^3/A, n)) /* Michael Somos Jul 13 2004 */
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