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 A204220 Expansion of f(-x^2, -x^3) * f(-x^2) / f(-x) in powers of x. 2
 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS f(a, b) := Sum_{k} a^((k^2+k)/2) * b^((k^2-k)/2) is Ramanujan's two-variable theta function and f(-x) := f(-x, -x^2). LINKS FORMULA Expansion of G(x) * f(-x^2) where G() is g.f. of A003114. Expansion of f(-x^13, -x^17) + x * f(-x^7, -x^23) in powers of x. Euler transform of period 10 sequence [ 1, -1, 0, 0, 0, 0, 0, -1, 1, -1, ...]. G.f.: Sum_{k} (-1)^k * x^(15*k^2) * (x^(2*k) + x^(8*k + 1)) = Product_{k>0} (1 - x^(10*k)) * (1 - x^(10*k -2)) * (1 - x^(10*k -8)) / ((1 - x^(10*k -1)) * (1 - x^(10*k -9))). |a(n)| is the characteristic function of A204221. The exponents in the q-series q * A(q^15) is the square of the numbers == +- 1 or +- 4 (mod 15). EXAMPLE 1 + x - x^8 - x^13 - x^17 - x^24 + x^45 + x^56 + x^64 + x^77 - x^112 + ... q + q^16 - q^121 - q^196 - q^256 - q^361 + q^676 + q^841 + q^961 + q^1156 + ... PROG (PARI) {a(n) = if( n<0, 0, polcoeff( prod( k=1, n, (1 - x^k) ^ ([1, -1, 1, 0, 0, 0, 0, 0, 1, -1][k%10 + 1]), 1 + x * O(x^n)), n))} CROSSREFS Cf. A003114, A010815. Sequence in context: A016373 A167700 A010057 * A214263 A016355 A016402 Adjacent sequences:  A204217 A204218 A204219 * A204221 A204222 A204223 KEYWORD sign AUTHOR Michael Somos, Jan 13 2012 STATUS approved

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