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A006709
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Expansion of a modular function.
(Formerly M0600)
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1
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1, -2, -3, -4, 22, 30, -12, -128, -147, 132, 548, 516, -552, -1924, -1572, 1784, 5790, 4410, -5180, -15608, -11406, 13712, 39128, 27528, -33518, -92682, -63156, 77284, 208636, 139026, -170272, -449904, -294741, 360872, 936836, 604440, -739228, -1892636
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OFFSET
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-2,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Expansion of ((1/q) * f(-q, -q^2)^2 * f(q, q^2) / psi(q^3)^3)^2 in powers of q where psi(), f(,) are Ramanujan theta functions. - Michael Somos, Jan 18 2015
Expansion of (eta(q) * eta(q^2))^2 * (eta(q^3)^10 / eta(q^6)^14) in powers of q. - Michael Somos, Sep 22 2005
Euler transform of period 6 sequence [ -2, -4, -12, -4, -2, 0, ...]. - Michael Somos, Sep 22 2005
G.f.: (x^-2) * (Product_{k>0} (1 - x^k)^2 * (1 - x^(2*k))^2 * (1 - x^(3*k))^10 / (1 - x^(6*k))^14).
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EXAMPLE
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G.f. = 1/q^2 - 2/q - 3 - 4*q + 22*q^2 + 30*q^3 - 12*q^4 - 128*q^5 +...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ ( (1/q) QPochhammer[ q] QPochhammer[ q^2] QPochhammer[ q^3]^5 / QPochhammer[ q^6]^7)^2, {q, 0, n}]; (* Michael Somos, Jan 18 2015 *)
a[ n_] := SeriesCoefficient[ ( EllipticTheta[ 4, 0, q^3]^2 EllipticTheta[ 4, 0, q^9] (2 / (EllipticTheta[ 4, 0, q^9] - EllipticTheta[ 4, 0, q]))^3)^2, {q, 0, 3 n}]; (* Michael Somos, Jan 18 2015 *)
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PROG
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(PARI) {a(n) = local(A); if ( n<-2, 0, n+=2; A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^2 + A)^2 * eta(x^3 + A)^10 / eta(x^6 + A)^14, n))}; /* Michael Somos, Sep 22 2005 */
(PARI) q='q+O('q^99); Vec((eta(q)*eta(q^2))^2*(eta(q^3)^10/eta(q^6)^14)) \\ Altug Alkan, Apr 03 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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