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A132211
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Coefficients of a Ramanujan q-series.
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1
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1, -1, 0, 0, 0, 0, -1, 1, -1, 1, -1, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -1, 1, -1, 0, 1, -1, 1, -2, 3, -4, 4, -5, 7, -8, 8, -9, 11, -12, 12, -13, 15, -16, 16, -17, 19, -20, 19, -20, 22, -22, 21, -21, 22, -22, 20, -19, 20, -19, 16, -14, 14, -12, 8, -5, 3, 0, -5, 10, -13, 17, -24, 30, -34, 40, -48, 55, -61, 68, -77, 86, -93, 101
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OFFSET
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0,12
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REFERENCES
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S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 10
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (-1)^k * x^(k*(k + 1)/2) / (x^2; x^2)_n.
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EXAMPLE
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G.f. = 1 - x - x^6 + x^7 - x^8 + x^9 - x^10 + 2*x^11 - 2*x^12 + 2*x^13 - 2*x^14 + ...
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MATHEMATICA
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a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ (-1)^k x^(k (k + 1)/2) / QPochhammer[ x^2, x^2, k], {k, 0, Sqrt[8 n + 1]}], {x, 0, n}]]; (* Michael Somos, Nov 01 2015 *)
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PROG
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(PARI) {a(n) = my(t); if( n<0, 0, t = 1 + x * O(x^n); polcoeff( sum(k=1, (sqrtint(8*n + 1) - 1)\2, t = -t * x^k / (1 - x^(2*k)) + x * O(x^n), 1), 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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