A112157 McKay-Thompson series of class 18i for the Monster group.

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

Offset: 0

Author

Michael Somos, Aug 28 2005

Keywords

• sign

Examples

			T18i = 1/q -2*q^5 -q^11 +4*q^17 -3*q^23 +7*q^35 -8*q^41 +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500 (terms 0..1000 from Seiichi Manyama)
• D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
• Index entries for McKay-Thompson series for Monster simple group

Programs

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 *)

PARI

N=66; x='x+O('x^N); Vec( (eta(x)/eta(x^3))^2 ) \\ Joerg Arndt, Apr 20 2013

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