|
|
A112157
|
|
McKay-Thompson series of class 18i for the Monster group.
|
|
3
|
|
|
1, -2, -1, 4, -3, 0, 7, -8, -3, 14, -14, -4, 26, -26, -7, 44, -41, -10, 73, -72, -20, 118, -109, -28, 182, -174, -47, 280, -260, -66, 419, -392, -102, 618, -568, -144, 898, -832, -216, 1292, -1178, -296, 1828, -1676, -429, 2568, -2334, -588, 3570, -3248, -822, 4920, -4446, -1114, 6722, -6084
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Euler transform of period 3 sequence [ -2,-2,0, ...]. - Vladeta Jovovic, Oct 20 2006
Expansion of q^(1/6)*(eta(q)/eta(q^3))^2 in powers of q. - G. C. Greubel, Jun 06 2018
|
|
EXAMPLE
|
T18i = 1/q -2*q^5 -q^11 +4*q^17 -3*q^23 +7*q^35 -8*q^41 +...
|
|
MAPLE
|
N := 60; series(mul(1+x^k+x^(2*k), k=1..N)^(-2), x=0, N); # Mark van Hoeij, Apr 19 2013
|
|
MATHEMATICA
|
QP = QPochhammer; s = (QP[q]/QP[q^3])^2 + O[q]^60; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015, adapted from PARI *)
|
|
PROG
|
(PARI) N=66; x='x+O('x^N); Vec( (eta(x)/eta(x^3))^2 ) \\ Joerg Arndt, Apr 20 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|