|
| |
|
|
A030183
|
|
McKay-Thompson series of class 7A for the Monster group with a(0) = 10.
|
|
2
| |
|
|
1, 10, 51, 204, 681, 1956, 5135, 12360, 28119, 60572, 125682, 251040, 487426, 920568, 1699611, 3070508, 5445510, 9490116, 16283793, 27537708, 45959775, 75760640, 123471327, 199081632, 317814988
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 66.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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.
|
|
|
LINKS
| Index entries for McKay-Thompson series for Monster simple group
|
|
|
FORMULA
| Expansion of Hauptmodul for X_0^{+}(7).
Expansion of (h + 7)^2 / h, where h = (eta(q) / eta(q^7))^4 in powers of q.
a(n) = A007264(n) = A045489(n) unless n = 0.
|
|
|
EXAMPLE
| 1/q + 10 + 51*q + 204*q^2 + 681*q^3 + 1956*q^4 + 5135*q^5 + 12360*q^6 + ...
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); A = (eta(x^7 + A) / eta(x + A))^4; polcoeff( (1 + 7 * x * A)^2 / A, n))} /* Michael Somos, Feb 02 2012 */
|
|
|
CROSSREFS
| Cf. A045489, A007264.
Sequence in context: A124162 A077044 A069038 * A135242 A041186 A058827
Adjacent sequences: A030180 A030181 A030182 * A030184 A030185 A030186
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
