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A262090
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Expansion of f(x^3, x^21) / f(-x^2, -x^4) where f(, ) is the Ramanujan general theta function.
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2
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1, 0, 1, 1, 2, 1, 3, 2, 5, 3, 7, 5, 11, 7, 15, 11, 22, 15, 30, 22, 42, 31, 56, 43, 77, 58, 101, 80, 135, 106, 177, 142, 232, 187, 299, 246, 388, 319, 495, 415, 634, 532, 803, 683, 1017, 869, 1277, 1103, 1605, 1390, 2000, 1751, 2492, 2189, 3087, 2733, 3819
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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Euler transform of period 48 sequence [ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, ...].
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EXAMPLE
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G.f. = 1 + x^2 + x^3 + 2*x^4 + x^5 + 3*x^6 + 2*x^7 + 5*x^8 + 3*x^9 + ...
G.f. = q^77 + q^173 + q^221 + 2*q^269 + q^317 + 3*q^365 + 2*q^413 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ -x^3, x^24] QPochhammer[ -x^21, x^24] QPochhammer[ x^24] / QPochhammer[ x^2], {x, 0, n}];
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PROG
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(PARI) {a(n) = if( n<0, 0, A = x * O(x^n); polcoeff( subst( prod(k=1, n\3, 1 - x^k * [1, 1, 0, 0, 0, 0, 0, 1][k%8 + 1], 1 + x * O(x^(n\3))), x, -x^3) / eta(x^2 + x * O(x^n)), n))};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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