A132211 Coefficients of a Ramanujan q-series.

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

Offset: 0

Author

Michael Somos, Aug 13 2007

Keywords

• sign

Examples

			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 + ...
		

References

• S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 10

Crossrefs

Convolution with A015128 is A143184. - Michael Somos, Dec 13 2022

Programs

Mathematica

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 *)

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))};

Formula

G.f.: Sum_{k>=0} (-1)^k * x^(k*(k + 1)/2) / (x^2; x^2)_n.