%I A143840
%S A143840 1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,2,0,0,0,0,0,2,0,0,3,0,0,1,0,
%T A143840 0,4,0,0,4,0,0,1,0,0,4,0,0,6,0,0,1,0,0,5,0,0,8,0,0,1,0,0,8,0,0,10,0,0,
               2,
%U A143840 0,0,11,0,0,14,0,0,4,0,0,14,0,0,19,0,0,4,0,0,17,0,0,24,0,0,4,0,0,23
%V A143840 1,1,0,1,0,0,1,0,0,-1,0,0,-1,0,0,0,0,0,1,0,0,2,0,0,0,0,0,-2,0,0,-3,0,0,
               -1,0,0,4,0,0,4,
%W A143840 0,0,1,0,0,-4,0,0,-6,0,0,-1,0,0,5,0,0,8,0,0,1,0,0,-8,0,0,-10,0,0,-2,0,
               0,11,0,0,14,0,0,
%X A143840 4,0,0,-14,0,0,-19,0,0,-4,0,0,17,0,0,24,0,0,4,0,0,-23
%N A143840 McKay-Thompson series of class 18D for the Monster group with a(0) = 
               1.
%F A143840 Expansion of psi(q) / (q * psi(q^9)) = 1 + chi(-q^9)^3 / (q * chi(-q^3)) 
               in powers of q where psi(), chi() are Ramanujan theta functions.
%F A143840 Expansion of eta(q^2)^2 * eta(q^9) / (eta(q) * eta(q^18)^2) in powers 
               of q.
%F A143840 Euler transform of period 18 sequence [ 1, -1, 1, -1, 1, -1, 1, -1, 0, 
               -1, 1, -1, 1, -1, 1, -1, 1, 0, ...].
%F A143840 G.f. is a period 1 Fourier series which satisfies f(-1/ (18 t)) = 3 g(t) 
               where q = exp(2 pi i t) and g() is g.f. for A128770.
%F A143840 G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v * (u^2 + 3) 
               - (u + v)^2.
%F A143840 G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = u * (u^2 - 3*u 
               + 3) * (v^2 - 3*v + 3) - v^3.
%F A143840 a(3*n + 1) = 0. a(3*n) = 0 unless n=0.
%F A143840 G.f.: 1 + x^(-1) * Product_{k>0} (1 - x^(18*k - 9))^3 / (1 - x^(6*k - 
               3)).
%e A143840 1/q + 1 + q^2 + q^5 - q^8 - q^11 + q^17 + 2*q^20 - 2*q^26 - 3*q^29 + 
               ...
%o A143840 (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 
               eta(x^2 + A)^2 * eta(x^9 + A) / (eta(x + A) * eta(x^18 + A)^2), n))}
%Y A143840 A139032(n) = a(2*n). A062242(n) = a(3*n - 1). A092848(n) = a(6*n + 2). 
               A132179(n) = a(6*n - 1). Convolution inverse of A124243.
%Y A143840 Sequence in context: A045833 A117896 A132976 this_sequence A028649 A097798 
               A065205
%Y A143840 Adjacent sequences: A143837 A143838 A143839 this_sequence A143841 A143842 
               A143843
%K A143840 sign
%O A143840 -1,22
%A A143840 Michael Somos, Sep 02 2008