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A185125
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Expansion of f(-x, x^5) in powers of x where f(,) is the Ramanujan general theta function.
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2
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1, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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a(n) is nonzero if and only if n is a number of A001082.
The exponents in the q-series for this sequence are the squares of the numbers of A001651.
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LINKS
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FORMULA
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Euler transform of period 24 sequence [ -1, 0, 0, 0, 1, 1, 1, 0, 0, -1, -1, -2, -1, -1, 0, 0, 1, 1, 1, 0, 0, 0, -1, -1, ...].
G.f.: Sum_{k in Z} (-1)^floor(k/2) * x^(k * (3*k + 2)).
a(4*n + 2) = a(4*n + 3) = a(5*n + 2) = a(5*n + 4) = a(8*n + 4) = 0. a(4*n + 1) = - A080902(n). a(8*n) = A010815(n).
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EXAMPLE
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G.f. = 1 - x + x^5 - x^8 - x^16 + x^21 - x^33 + x^40 + x^56 - x^65 + x^85 + ...
G.f. = q - q^4 + q^16 - q^25 - q^49 + q^64 - q^100 + q^121 + q^169 - q^196 + ...
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MATHEMATICA
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a[ n_] := SeriesCoefficient[ QPochhammer[ x, -x^6] QPochhammer[ -x^5, -x^6] QPochhammer[ -x^6], {x, 0, n}]; (* Michael Somos, Jun 30 2015 *)
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PROG
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(PARI) {a(n) = my(m); if( issquare( 3*n + 1, &m), (m%3!=0) * (-1)^((m+3) \ 6 + n), 0)};
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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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