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A280328
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Expansion of f(-x)^3 * f(-x^2) * chi(-x^3)^3 in powers of x where chi(), f() are Ramanujan theta functions.
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3
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1, -3, -1, 5, 8, 1, -28, -11, 10, 41, 41, -26, -53, -84, 21, 101, 76, -3, -129, -99, 14, 190, 187, -59, -299, -263, 62, 336, 340, -27, -459, -370, 111, 645, 518, -228, -774, -806, 179, 973, 882, -147, -1233, -955, 291, 1565, 1325, -395, -1883, -1767, 338, 2318
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Expansion of q * eta(q^6)^3 * eta(q^12) * eta(q^18)^3 / eta(q^36)^3 in powers of q^6.
Euler transform of period 6 sequence [-3, -4, -6, -4, -3, -4, ...].
a(5*n + 1) / a(1) == A000727(n) (mod 5). a(125*n + 21) / a(21) == A000727(n) (mod 25).
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EXAMPLE
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G.f. = 1 - 3*x - x^2 + 5*x^3 + 8*x^4 + x^5 - 28*x^6 - 11*x^7 + 10*x^8 + ...
G.f. = q^-1 - 3*q^5 - q^11 + 5*q^17 + 8*q^23 + q^29 - 28*q^35 - 11*q^41 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x]^3 QPochhammer[ x^2] QPochhammer[ x^3, x^6]^3, {x, 0, n}];
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PROG
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(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^2 + A) * eta(x^3 + A)^3 / eta(x^6 + A)^3, 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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