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A280384
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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, 1994
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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^12)^10 * eta(q^36)^6 / (eta(q^6)^3 * eta(q^18)^3 * eta(q^24)^3 * eta(q^72)^3) in powers of q^6.
Euler transform of period 12 sequence [3, -7, 6, -4, 3, -10, 3, -4, 6, -7, 3, -4, ...].
a(5*n + 1) / a(1) == A187076(n) (mod 5). a(125*n + 21) / a(21) == A187076(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^2 + A)^10 * eta(x^6 + A)^6 / (eta(x + A)^3 * eta(x^3 + A)^3 * eta(x^4 + A)^3 * eta(x^12 + 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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