login
Expansion of q^(-7/12)eta(q)eta(q^6)^3/(eta(q^2)eta(q^3)) in powers of q.
1

%I #5 Apr 30 2014 01:38:21

%S 1,-1,0,0,0,-1,-1,1,1,0,0,1,-1,1,-1,0,1,1,0,0,-1,-1,-1,0,0,0,0,1,-1,0,

%T 1,-1,0,0,0,-1,0,0,1,1,1,0,1,-1,0,1,0,-1,0,0,1,-1,-1,0,0,0,1,0,1,0,0,

%U 0,-1,-2,0,-1,0,0,-1,0,1,1,-1,1,0,-1,0,2,0,0,-1,0,1,0,0,-1,1,0,-1,0,-1,2,0,1,0,0,1,1,0,0,0,0,-1,0,0

%N Expansion of q^(-7/12)eta(q)eta(q^6)^3/(eta(q^2)eta(q^3)) in powers of q.

%C |a(n)|<2 if n<63, |a(n)|<3 if n<742, |a(n)|<4 if n<8456.

%F Euler transform of period 6 sequence [ -1, 0, 0, 0, -1, -2, ...].

%F G.f.: Product_{k>0} (1-x^(6k))^2*(1-x^(6k-1))*(1-x^(6k-5)).

%o (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^6+A)^3/ eta(x^2+A)/eta(x^3+A), n))}

%K sign

%O 0,64

%A _Michael Somos_, Nov 05 2005