%I #20 Mar 12 2021 22:24:46
%S 1,-1,0,2,-1,-2,4,-2,-2,6,-4,-4,10,-6,-8,16,-9,-10,24,-14,-16,36,-20,
%T -24,53,-30,-32,76,-43,-48,108,-60,-68,150,-84,-92,206,-114,-128,280,
%U -155,-172,376,-208,-228,504,-276,-304,668,-366,-400,878,-480,-524,1148
%N McKay-Thompson series of class 24C for the Monster group with a(0) = -1.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A206299/b206299.txt">Table of n, a(n) for n = -1..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of (1/q) * chi(q) * chi(q^12)^3 / (chi(q^3)^3 * chi(q^4)) in powers of q where chi() is a Ramanujan theta function.
%F Expansion of c(q^2)*c(q^4)/(c(q)*c(q^8)) in powers of q where c() is a cubic AGM theta function.
%F Euler transform of period 24 sequence [ -1, 0, 2, 1, -1, 0, -1, 0, 2, 0, -1, -2, -1, 0, 2, 0, -1, 0, -1, 1, 2, 0, -1, 0, ...].
%F a(n) = A058573(n) unless n = 0.
%F Expansion of eta(q)*eta(q^6)^3*eta(q^8)*eta(q^12)^3/(eta(q^2)*eta(q^3)^3* eta(q^4)*eta(q^24)^3) in powers of q. - _G. C. Greubel_, Jun 20 2018
%e 1/q - 1 + 2*q^2 - q^3 - 2*q^4 + 4*q^5 - 2*q^6 - 2*q^7 + 6*q^8 - 4*q^9 + ...
%t QP = QPochhammer; s = QP[q]*QP[q^6]^3*QP[q^8]*(QP[q^12]^3/(QP[q^2]* QP[q^3]^3*QP[q^4]*QP[q^24]^3)) + O[q]^60; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 16 2015, adapted from PARI *)
%o (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^3 * eta(x^8 + A) * eta(x^12 + A)^3 / (eta(x^2 + A) * eta(x^3 + A)^3 * eta(x^4 +A ) * eta(x^24 + A)^3), n))}
%Y Cf. A058573, A206298, A184990.
%K sign
%O -1,4
%A _Michael Somos_, Feb 05 2012