Search: id:A007240
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%I A007240 M5179 N2372
%S A007240 1,24,196884,21493760,864299970,20245856256,333202640600,4252023300096,
%T A007240 44656994071935,401490886656000,3176440229784420,22567393309593600,
%U A007240 146211911499519294,874313719685775360,4872010111798142520,25497827389410525184
%N A007240 McKay-Thompson series of class 1A for Monster; another version of the 
               j-function.
%C A007240 Changing the term 24 to 744 gives the classical j-function: see A000521 
               for much more information.
%C A007240 "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]
%D A007240 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007240 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A007240 R. E. Borcherds, Review of "Moonshine Beyond the Monster ..." (Cambridge, 
               2006), Bull. Amer. Math. Soc., 45 (2008), 675-679.
%D A007240 H. Cohen, Course in Computational Number Theory, page 379.
%D A007240 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. 
               Soc. 11 (1979) 308-339.
%D A007240 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%D A007240 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.
%D A007240 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.
%D A007240 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, 
               p. 56.
%D A007240 J. G. Thompson, Some numerology between the Fischer-Griess Monster and 
               the elliptic modular function, Bull. London Math. Soc., 11 (1979), 
               352-353.
%D A007240 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 ].
%H A007240 N. J. A. Sloane, <a href="b007240.txt">Table of n, a(n) for n = -1..10000</
               a>
%H A007240 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%H A007240 A. Berkovich and H. Yesilyurt, <a href="http://arXiv.org/abs/math.NT/
               0611300">Ramanujan's identities and representation of integers by 
               certain binary and quaternary quadratic forms</a>
%H A007240 B. H. Lian and J. L. Wiczer, <a href="http://arXiv.org/abs/math.NT/0611291">
               Genus Zero Modular Functions</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha135.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha136.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha137.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha139.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha140.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha141.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha142.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha143.htm">Factorizations of many number sequences</a>
%H A007240 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha144.htm">Factorizations of many number sequences</a>
%e A007240 1/q+24+196884*q+...
%Y A007240 Cf. A000521, A014708.
%Y A007240 Sequence in context: A048057 A058550 A145200 this_sequence A061526 A159422 
               A028371
%Y A007240 Adjacent sequences: A007237 A007238 A007239 this_sequence A007241 A007242 
               A007243
%K A007240 nonn,easy,nice
%O A007240 -1,2
%A A007240 N. J. A. Sloane (njas(AT)research.att.com).

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