-1,3

Normalized McKay-Thompson series of class 1A for the Monster group.

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

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.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

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.

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. G. Thompson, Some numerology between the Fischer-Griess Monster and the elliptic modular function, Bull. London Math. Soc., 11 (1979), 352-353.

N. J. A. Sloane, Table of n, a(n) for n = -1..1000

Index entries for McKay-Thompson series for Monster simple group

Hisanori Mishima, Factorizations of many number sequences

I. B. Frenkel et al., A natural representation of the Fischer-Griess Monster with the modular function J as character

V. G. Kac, A remark on the Conway-Norton Conjecture about the "Monster" simple group

University of Sheffield, Department of Pure Mathematics, Is e^(Pi*Sqrt(163)) an integer?

A007245^3/q - 744.

T1A = 1/q + 196884q + 21493760q^2 + 864299970q^3 + ...

(PARI) a(n)=if(n<1, n==-1, polcoeff(ellj(x+O(x^(n+3))), n)) /* Michael Somos Jan 19 2005 */

Cf. A000521, A007240, A027653, A003173, A069014.

Sequence in context: A024211 A113919 A001379 this_sequence A035230 A099818 A043592

Adjacent sequences: A014705 A014706 A014707 this_sequence A014709 A014710 A014711

easy,nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).