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 A132979 Expansion of psi(q^3) / psi(q)^3 in powers of q where psi() is a Ramanujan theta function. 3
 1, -3, 6, -12, 24, -45, 78, -132, 222, -363, 576, -900, 1392, -2121, 3180, -4716, 6936, -10098, 14550, -20796, 29520, -41595, 58176, -80856, 111750, -153561, 209820, -285240, 385968, -519840, 696960, -930516, 1237470, -1639314, 2163456, -2845080, 3728904, -4871211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). LINKS Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of eta(q)^3 * eta(q^6)^2 / ( eta(q^2)^6 * eta(q^3) ) in powers of q. Euler transform of period 6 sequence [ -3, 3, -2, 3, -3, 2, ...]. G.f.: Product_{k>0} (1 + x^(3*k)) * (1 - x^(6*k)) / ( (1 + x^k) * (1 - x^(2*k)) )^3. EXAMPLE 1 - 3*q + 6*q^2 - 12*q^3 + 24*q^4 - 45*q^5 + 78*q^6 - 132*q^7 + ... PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^6 + A )^2 / ( eta(x^2 + A)^6 * eta(x^3 + A) ), n))} CROSSREFS (-1)^n * A132974(n) = a(n). Convolution invserse of A107760. Sequence in context: A039695 A079079 A132974 * A163314 A018183 A196787 Adjacent sequences:  A132976 A132977 A132978 * A132980 A132981 A132982 KEYWORD sign AUTHOR Michael Somos, Sep 07 2007 STATUS approved

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