|
Search: id:A058688
|
|
|
| A058688 |
|
McKay-Thompson series of class 46A for the Monster group. |
|
+0
2
|
|
| 1, 0, 0, -1, 1, -1, 1, -1, 2, -2, 2, -2, 3, -3, 3, -4, 5, -5, 5, -6, 7, -8, 8, -10, 12, -12, 13, -15, 17, -18, 19, -22, 25, -27, 28, -32, 36, -38, 41, -46, 51, -54, 58, -64, 71, -76, 81, -89, 99, -105, 112, -123, 134, -143, 153, -167, 182, -194, 207, -225, 244, -260, 277, -301, 325, -346, 369, -398, 429, -458
(list; graph; listen)
|
|
|
OFFSET
|
-1,9
|
|
|
COMMENT
|
Also McKay-Thompson series of class 46B for the Monster group.
|
|
REFERENCES
|
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
|
|
LINKS
|
Index entries for McKay-Thompson series for Monster simple group
|
|
FORMULA
|
Expansion of 1+(1/q)chi(-q)chi(-q^23) in powers of q where chi() is a Ramanujan theta function. - Michael Somos Jun 07 2006
G.f.: 1 + (1/x)*Product_{k>0} 1/((1+x^k)(1+x^(23k))).
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)= v^2 -v +2 -2*u +u^2 -v*u^2 . - Michael Somos Feb 14 2007
|
|
EXAMPLE
|
T46A = 1/q -q^2 +q^3 -q^4 +q^5 -q^6 +2*q^7 -2*q^8 +2*q^9 +...
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<-1, 0, n++; A=x*O(x^n); polcoeff( x+ eta(x+A)*eta(x^23+A)/ eta(x^2+A)/eta(x^46+A), n))} /* Michael Somos Feb 14 2007 */
|
|
CROSSREFS
|
Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
Sequence in context: A000700 A081362 A112216 this_sequence A132322 A018118 A029084
Adjacent sequences: A058685 A058686 A058687 this_sequence A058689 A058690 A058691
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Nov 27, 2000
|
|
|
Search completed in 0.002 seconds
|
