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A096661
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Fine's numbers J(n).
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4
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0, 0, -1, 1, -1, 1, -1, 2, -1, 0, -1, 2, -1, 0, -1, 1, -1, 0, 0, 2, -1, -1, -1, 2, 0, 0, 0, 1, -1, 0, -1, 2, -1, -1, 0, 2, 0, 0, -2, 1, -2, 0, 1, 2, -1, 0, -2, 2, 0, 0, -1, 1, -1, 0, -1, 3, -1, 0, 0, 2, -1, 0, -2, 0, -1, 1, 1, 2, -1, 0, -3, 2, 0, 0, 0, 1, -1, -1, -1, 2, -2, 0, 0, 2, 1, 1, -2, 0, -1, 0, 0, 1, -1, 0, -2, 3, 0, 0, 1, 0, -1, 0, -1, 2, -1
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OFFSET
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0,8
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REFERENCES
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N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 62, Eq. (27.1).
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LINKS
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FORMULA
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G.f.: Sum_{n >= 1} (-1)^n*q^((3*n^2+n)/2)/(1+q^n).
Dragonette's gamma(n) = A064053(n) = 4*a(n) if n>0.
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EXAMPLE
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G.f. = - x^2 + x^3 - x^4 + x^5 - x^6 + 2*x^7 - x^8 - x^10 + 2*x^11 - x^12 + ...
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MAPLE
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add( (-1)^n*q^((3*n^2+n)/2)/(1+q^n), n=1..10);
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MATHEMATICA
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a[n_]:= SeriesCoefficient[Sum[(-1)^k*q^((3*k^2 + k)/2)/(1 + q^k), {k, 1, 2*nmax}], {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 18 2018 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=1, (sqrtint(24*n + 1) - 1) \ 6, (-1)^k * x^((3*k^2 + k)/2) / (1 + x^k), x * O(x^n)), n))}; /* Michael Somos, Mar 13 2006 */
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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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