%I
%S 1,1,2,0,1,0,0,0,2,0,2,0,2,0,4,0,3,0,4,0,8,0,4,0,5,0,14,0,7,0,8,
%T 0,20,0,12,0,14,0,28,0,17,0,20,0,44,0,24,0,28,0,66,0,36,0,40,0,
%U 90,0,52,0,56,0,124,0,71,0,80,0,176,0,96,0,109,0,244,0,133,0,144
%N McKayThompson series of class 12I for the Monster group with a(0) = 1.
%D J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi's identity and the AGM, Trans. Amer. Math. Soc., 323 (1991), no. 2, 691701.
%D D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 51755193 (1994).
%F Expansion of c(q) / c(q^4) in powers of q where c() is a cubic AGM function.
%F Expansion of eta(q^3)^3 * eta(q^4) / (eta(q) * eta(q^12)^3) in powers of q.
%F Euler transform of period 12 sequence [ 1, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, ...].
%F Convolution inverse of A123649.
%F a(2*n) = 0 unless n=0. a(2*n  1) = A058487(n).
%e 1/q + 1 + 2*q + q^3  2*q^7  2*q^9 + 2*q^11 + 4*q^13 + 3*q^15  4*q^17 + ...
%o (PARI) {a(n) = local(A); if( n<1, 0, n++; A = x * O(x^n); polcoeff( eta(x^3 + A)^3 * eta(x^4 + A) / (eta(x + A) * eta(x^12 + A)^3) , n))}
%Y Cf. A058487, A123649.
%K sign
%O 1,3
%A Michael Somos, Mar 05 2011
