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A233431
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Expansion of q * f(-q^7)^3 * f(-q^2, -q^5) / f(-x^3, -q^4)^2 in powers of q where f() is a Ramanujan theta function.
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1
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1, 0, -1, 2, 2, -3, 1, 3, -2, -1, 3, 0, 0, 0, 1, 2, -1, -2, 2, 0, -1, 3, 0, -1, 4, 0, -3, 2, 2, -4, -1, 4, 2, -3, 2, 2, 0, -1, 0, 2, 0, -3, 2, 4, -2, 1, 2, -3, 1, 2, -4, 0, 3, -2, 3, 3, 1, 0, -1, 0, 2, -3, -2, 5, 0, -1, 3, 0, -3, -1, 2, 0, -1, 1, 4, 0, 3, 0
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OFFSET
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1,4
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COMMENTS
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LINKS
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FORMULA
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Euler transform of period 7 sequence [ 0, -1, 2, 2, -1, 0, -2, ...].
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EXAMPLE
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G.f. = q - q^3 + 2*q^4 + 2*q^5 - 3*q^6 + q^7 + 3*q^8 - 2*q^9 - q^10 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ q Product[ (1 - q^k)^{0, 1, -2, -2, 1, 0, 2, 2}[[Mod[k, 7, 1]]], {k, n}], {q, 0, n}]
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PROG
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(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( prod( k=1, n, (1 - x^k + A)^[ 2, 0, 1, -2, -2, 1, 0, 2][k%7 + 1]), n))}
(Sage) ModularForms( Gamma1(7), 1, prec=70).1
(Magma) Basis( ModularForms( Gamma1(7), 1), 70) [2]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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