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A260165
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Expansion of f(x, x^2) * f(x, x^3)^3 in powers of x where f(, ) is Ramanujan's general theta function.
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2
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1, 4, 7, 10, 13, 14, 18, 22, 25, 28, 26, 34, 37, 36, 43, 38, 49, 54, 56, 58, 43, 64, 67, 70, 73, 62, 79, 72, 90, 88, 74, 98, 97, 100, 90, 84, 108, 112, 115, 126, 98, 108, 127, 130, 140, 110, 139, 142, 126, 148, 133, 154, 152, 160, 163, 108, 169, 182, 175, 180
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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 phi(-x^3) * f(-x^2)^5 / phi(-x)^2 in powers of x where phi(), f() are Ramanujan theta functions.
Expansion of q^(-5/12) * eta(q^2)^7 * eta(q^3)^2 / (eta(q)^4 * eta(q^6)) in powers of q.
Euler transform of period 6 sequence [4, -3, 2, -3, 4, -4, ...].
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EXAMPLE
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G.f. = 1 + 4*x + 7*x^2 + 10*x^3 + 13*x^4 + 14*x^5 + 18*x^6 + 22*x^7 + 25*x^8 + ...
G.f. = q^5 + 4*q^17 + 7*q^29 + 10*q^41 + 13*q^53 + 14*q^65 + 18*q^77 + 22*q^89 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, x^3] QPochhammer[ x^2]^5 / EllipticTheta[ 4, 0, x]^2, {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)^7 * eta(x^3 + A)^2 / (eta(x + A)^4 * eta(x^6 + A)), 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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