|
Search: id:A102314
|
|
|
| A102314 |
|
McKay-Thompson series of class 42C for the Monster group. |
|
+0
1
|
|
| 1, -1, 0, -1, 1, -1, 1, -2, 3, -2, 3, -3, 4, -4, 4, -6, 7, -7, 7, -9, 10, -12, 13, -14, 17, -18, 19, -22, 26, -28, 29, -34, 38, -41, 44, -50, 57, -60, 65, -72, 81, -86, 94, -105, 114, -124, 133, -146, 161, -174, 187, -204, 224, -240, 258, -282, 309, -332, 354, -386, 419, -450, 481, -524, 569, -606, 651, -703
(list; graph; listen)
|
|
|
OFFSET
|
0,8
|
|
|
REFERENCES
|
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
|
|
FORMULA
|
Expansion of q eta(q^3)eta(q^21)/(eta(q^6) eta(q^42)) in powers of q^3.
Euler transform of period 14 sequence [ -1, 0, -1, 0, -1, 0, -2, 0, -1, 0, -1, 0, -1, 0, ...].
Given g.f. A(x), then B(x)=A(x^3)/x satisfies 0=f(B(x), B(x^2)) where f(u, v)=v^2-u^2v-2u.
|
|
EXAMPLE
|
T42C = 1/q - q^2 - q^8 + q^11 - q^14 + q^17 - 2*q^20 + 3*q^23 - 2*q^26 + ...
|
|
PROGRAM
|
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^7+A)/eta(x^2+A)/eta(x^14+A), n))}
|
|
CROSSREFS
|
Sequence in context: A030397 A082597 A112212 this_sequence A031248 A030582 A036762
Adjacent sequences: A102311 A102312 A102313 this_sequence A102315 A102316 A102317
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Michael Somos, Jan 03 2005
|
|
|
Search completed in 0.002 seconds
|
