A209457 Expansion of x^7*Product_{i>=0} ((1 + x^(2*i - 1))*(1 - x^(4*i - 5))).

1, 1, -1, -1, 0, 0, -1, -1, 1, 2, 0, -2, 0, 2, 0, -3, 0, 4, 1, -4, -2, 4, 2, -5, -3, 6, 5, -5, -6, 5, 6, -7, -8, 7, 11, -5, -12, 5, 13, -6, -16, 5, 19, -3, -21, 2, 23, -2, -26, 0, 30, 4, -32, -6, 34, 7, -39, -12, 43, 18

Offset: 0

Author

Roger L. Bagula, Mar 09 2012

Keywords

• sign

Comments

Expansion of x^7 QPochhammer[1/x^5, x^4] QPochhammer[-(1/x), x^2].

Examples

			Series[x^7 QPochhammer[1/x^5, x^4] QPochhammer[-(1/x), x^2], {x, 0, 10}] = 1+x-x^2-x^3-x^6-x^7+x^8+2*x^9+O[x]^11.
		

References

• George E. Andrews, Number Theory, Dover Publications, N.Y., 1971, 164-165.
• Samuel I. Goldberg, Curvature and Homology, Dover, New York, 1998, 144.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A207944.

Programs

Mathematica

Table[SeriesCoefficient[Series[x^7*Product[(1 + x^(2*i - 1))*(1 - x^(4*i - 5)), {i, 0, Infinity}], {x, 0, 100}], n], {n, 0, 100}]