|
Search: id:A007247
|
|
|
| A007247 |
|
McKay-Thompson series of class 4B for Monster.
(Formerly M5305)
|
|
+0
3
|
|
| 1, 52, 834, 4760, 24703, 94980, 343998, 1077496, 3222915, 8844712, 23381058, 58359168, 141244796, 327974700, 742169724, 1627202744, 3490345477, 7301071680, 14987511560, 30138820888, 59623576440, 115928963656
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
McKay, John; Strauss, Hubertus. The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
D. Ford, J. McKay and S. P. Norton, ``More on replicable functions,'' Commun. Algebra 22, No. 13, 5175-5193 (1994).
|
|
FORMULA
|
Expansion of 4q(1+k'^2)^2/(k'k^2) in powers of q^2 where k is the Jacobian elliptic modulus, k' the complementary modulus and q is the nome.
|
|
EXAMPLE
|
T4B = 1/q + 52*q + 834*q^3 + 4760*q^5 + 24703*q^7 + 94980*q^9 + ...
|
|
PROGRAM
|
(PARI) a(n)=local(A); if(n<0, 0, A=prod(k=1, (n+1)\2, 1-x^(2*k-1), 1+x*O(x^n))^12; polcoeff(64*x/A+A, n))
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); A=(eta(x+A)/eta(x^2+A))^12; polcoeff(A+64*x/A, n))} /* Michael Somos Nov 11 2006 */
|
|
CROSSREFS
|
Sequence in context: A005946 A000527 A100413 this_sequence A083936 A133238 A130000
Adjacent sequences: A007244 A007245 A007246 this_sequence A007248 A007249 A007250
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
