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A164614
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Expansion of (chi(q) / chi^3(q^3))^2 in powers of q where chi() is a Ramanujan theta function.
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2
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1, 2, 1, -4, -8, -2, 14, 24, 6, -38, -63, -16, 92, 150, 36, -208, -329, -78, 440, 684, 160, -884, -1358, -312, 1710, 2592, 590, -3196, -4796, -1082, 5800, 8632, 1929, -10270, -15162, -3364, 17784, 26078, 5750, -30192, -44010, -9644, 50369, 73012, 15916, -82698, -119280, -25880, 133818
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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).
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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
| Expansion of q^(-2/3) * (eta(q^2)^2 * eta(q^3)^3 * eta(q^12)^3 / (eta(q) * eta(q^4) * eta(q^6)^6))^2 in powers of q.
Euler transform of period 12 sequence [ 2, -2, -4, 0, 2, 4, 2, 0, -4, -2, 2, 0, ...].
Convolution square of A128111.
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EXAMPLE
| q^2 + 2*q^5 + q^8 - 4*q^11 - 8*q^14 - 2*q^17 + 14*q^20 + 24*q^23 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A)^3 / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A)^6))^2, n))}
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CROSSREFS
| Sequence in context: A071951 A160323 A128411 * A094511 A193730 A026204
Adjacent sequences: A164611 A164612 A164613 * A164615 A164616 A164617
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 17 2009
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