Search: id:A014708
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%I A014708
%S A014708 1,0,196884,21493760,864299970,20245856256,333202640600,4252023300096,
%T A014708 44656994071935,401490886656000,3176440229784420,22567393309593600,
%U A014708 146211911499519294,874313719685775360,4872010111798142520,25497827389410525184
%N A014708 Coefficients of the modular function J = j - 744.
%C A014708 Normalized McKay-Thompson series of class 1A for the Monster group.
%C A014708 If n=A003173(k)=3 (mod 4) then j(-exp(-sqrt(n) pi)) is an integer such 
               that exp(sqrt(n) pi) is very close to an integer, cf. A069014, A056581 
               and references therein. - M. F. Hasler, Apr 15 2008
%D A014708 H. Cohen, Course in Computational Number Theory, page 379.
%D A014708 J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. 
               Soc. 11 (1979) 308-339.
%D A014708 D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. 
               Algebra 22, No. 13, 5175-5193 (1994).
%D A014708 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 A014708 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 A014708 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, 
               p. 56.
%D A014708 J. G. Thompson, Some numerology between the Fischer-Griess Monster and 
               the elliptic modular function, Bull. London Math. Soc., 11 (1979), 
               352-353.
%H A014708 N. J. A. Sloane, <a href="b014708.txt">Table of n, a(n) for n = -1..1000</
               a>
%H A014708 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%H A014708 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A014708 I. B. Frenkel et al., <a href="http://www.pnas.org/cgi/reprint/81/10/
               3256.pdf">A natural representation of the Fischer-Griess Monster 
               with the modular function J as character</a>
%H A014708 V. G. Kac, <a href="http://www.pnas.org/cgi/reprint/77/9/5048.pdf">A 
               remark on the Conway-Norton Conjecture about the "Monster" simple 
               group</a>
%H A014708 University of Sheffield, Department of Pure Mathematics, <a href="http:/
               /www.shef.ac.uk/~puremath/theorems/nearint.html">Is e^(Pi*Sqrt(163)) 
               an integer?</a>
%F A014708 A007245^3/q - 744.
%e A014708 T1A = 1/q + 196884q + 21493760q^2 + 864299970q^3 + ...
%o A014708 (PARI) a(n)=if(n<1,n==-1,polcoeff(ellj(x+O(x^(n+3))),n)) /* Michael Somos 
               Jan 19 2005 */
%Y A014708 Cf. A000521, A007240, A027653, A003173, A069014.
%Y A014708 Sequence in context: A024211 A113919 A001379 this_sequence A035230 A099818 
               A043592
%Y A014708 Adjacent sequences: A014705 A014706 A014707 this_sequence A014709 A014710 
               A014711
%K A014708 easy,nonn,nice
%O A014708 -1,3
%A A014708 N. J. A. Sloane (njas(AT)research.att.com).

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