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%I #6 Apr 30 2014 01:35:19
%S 1,-1,-1,1,-1,0,2,-1,-1,3,-2,-1,4,-2,-3,4,-3,-3,8,-4,-5,9,-4,-6,13,-6,
%T -7,14,-10,-9,20,-9,-12,24,-13,-13,32,-16,-19,39,-23,-24,50,-26,-27,
%U 60,-35,-34,78,-41,-42,91,-49,-54,111,-60,-65,138,-73,-78,167,-84,-95,199,-107,-111,236,-128,-135,282,-147,-159,338
%N Expansion of (eta(q) * eta(q^39)) / (eta(q^3) * eta(q^13)) in powers of q.
%F Euler transform of period 39 sequence [ -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, 0, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, -1, -1, 0, ...].
%F G.f. A(x) satisfies 0 = f(A(x), A(x^2)) = f(1/A(x), 1/A(x^2)) where f(u, v)=u^3 + v^3 + 2*u*v*(u + v) - u^2*v^2 - u*v.
%F G.f.: x * Product_{k>0} (1 - x^k) * (1 - x^(3*9k)) / ((1 - x^(3*k)) * (1 - x^(13*k))).
%F Convolution inverse of A094362.
%e q - q^2 - q^3 + q^4 - q^5 + 2*q^7 - q^8 - q^9 + 3*q^10 - 2*q^11 - q^12 + 4*q^13 + ...
%o (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^39 + A) / (eta(x^3 + A) * eta(x^13 + A)), n))}
%Y Cf. A094362.
%K sign
%O 1,7
%A _Michael Somos_, May 03 2004
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