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A083650
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Expansion of f(-x, x^3) * phi(x^2) in powers of x where phi(), f() are Ramanujan theta functions.
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7
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1, -1, 2, -1, 0, 2, -1, 0, 0, -2, -1, 2, -2, 0, -2, 1, 0, 2, 0, -2, 0, 1, 0, 0, -2, 0, 0, 0, -1, -2, 2, 0, 2, 0, 0, 2, 3, 0, 0, -2, 0, 0, -2, 0, 2, -1, 2, 0, 0, 0, 2, -2, 0, -2, 2, 1, -2, 2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, -2, 2, 0, -2, 2, 0, -2, -1, 0, -2, 0, -2, 0, -2, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 0, 0, -2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
Essentially the expansion of eta(q)*eta(q^2). Cf. A010815. - N. J. A. Sloane, Feb 18 2010
A030204, A083650 and A138514 are the same except for signs. - N. J. A. Sloane, May 07 2010
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Euler transform of period 16 sequence [ -1, 2, 1, -2, 1, 1, -1, -3, -1, 1, 1, -2, 1, 2, -1, -2, ...].
G.f.: (Sum_{k>=0} (-1)^(k + [k/4]) * x^(k*(k+1)/2)) * (Sum_k x^(2*k^2)).
(-1)^[n/2] * a(n) = A030204(n).
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EXAMPLE
| 1 - x + 2*x^2 - x^3 + 2*x^5 - x^6 - 2*x^9 - x^10 + 2*x^11 - 2*x^12 - 2*x^14 + ...
q - q^9 + 2*q^17 - q^25 + 2*q^41 - q^49 + 2*q^73 - q^81 + 2*q^89 - 2*q^97 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); (-1)^(n\2) * polcoeff( eta(x + A) * eta(x^2 + A), n))} /* Michael Somos Mar, 02 2010 */
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CROSSREFS
| Cf. A030204, A143433.
Sequence in context: A190893 A030204 * A138514 A143540 A030200 A095734
Adjacent sequences: A083647 A083648 A083649 * A083651 A083652 A083653
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KEYWORD
| sign
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AUTHOR
| Michael Somos, May 01 2003, revised Mar 02 2010
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