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 A107064 Expansion of q^(-17/24) * (eta(q) * eta(q^6)^4) / (eta(q^2) * eta(q^3)^2) in powers of q. 0

%I

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

%T 0,-1,0,-1,1,-1,-1,0,1,-1,1,0,-1,1,0,1,0,0,0,1,-1,-2,0,1,0,0,1,0,1,1,

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

%N Expansion of q^(-17/24) * (eta(q) * eta(q^6)^4) / (eta(q^2) * eta(q^3)^2) in powers of q.

%C Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).

%H M. Somos, <a href="http://cis.csuohio.edu/~somos/multiq.pdf">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 Euler transform of period 6 sequence [ -1, 0, 1, 0, -1, -2, ...].

%F G.f.: Product_{k>0} ((1-x^(6k))(1+x^(3k)))^2/(1+x^k).

%F Expansion of psi(q^3)^2 * chi(-q) in powers of q where psi(), chi() are Ramanujan theta functions.

%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^6 + A)^4 / eta(x^2 + A) / eta(x^3 + A)^2, n))}

%Y Cf. A030204(3n+2)=-2a(n).

%K sign

%O 0,52

%A Michael Somos, May 10 2005

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Last modified May 21 11:29 EDT 2013. Contains 225478 sequences.