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A262933
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Expansion of f(-q^2, -q^5)^3 / (f(-q^1, -q^6) * f(-q^3, -q^4)^2) in powers of q where f(, ) is Ramanujan's general theta function.
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4
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1, 1, -2, 0, 5, -4, -7, 12, 4, -22, 7, 29, -26, -28, 52, 14, -82, 21, 106, -85, -105, 175, 53, -268, 70, 326, -264, -301, 505, 142, -742, 189, 885, -698, -805, 1323, 374, -1906, 483, 2205, -1732, -1946, 3185, 884, -4486, 1120, 5119, -3972, -4473, 7229, 2004
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OFFSET
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0,3
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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 [ 1, -3, 2, 2, -3, 1, 0, ...].
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EXAMPLE
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G.f. = 1 + q - 2*q^2 + 5*q^4 - 4*q^5 - 7*q^6 + 12*q^7 + 4*q^8 - 22*q^9 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^{-1, 3, -2, -2, 3, -1, 0}[[Mod[k, 7, 1]]], {k, n}], {x, 0, n}];
(* alternative program *)
QP:= QPochhammer; a[n_]:= SeriesCoefficient[(QP[q^2, q^7]*QP[q^5, q^7])^3/ (QP[q, q^7]*QP[q^6, q^7]*QP[q^3, q^7]^2*QP[q^4, q^7]^2), {q, 0, n}];
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PROG
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(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^[0, -1, 3, -2, -2, 3, -1][k%7 + 1]), n))};
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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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