A207944 -id:A207944 - cp's OEIS frontend

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

Roger L. Bagula, Mar 09 2012

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

			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.

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

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

Cf. A207944.

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}]

A208150 Expansion of (1 + 2Product_{i>=1} (1 + x^(8i - 1)))/(-1 + Product_{i>=1} (1 - x^(8*i - 1))).

Original entry on oeis.org

-2, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -4, 3, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, -4, 2, 3, 0, 0, 0, 0, 0, -3, -9, -3, 0, 0, 0, 0, -4, 1, 5, 3, 0, 0, 0, 0, 1, -15, -9, -3, 0, 0, 0, -4, 0, 6, 5, 3, 0, 0, 0, 5, -20, -21, -12, -3, 0, 0, -4, -1, 16

Offset: 0

Roger L. Bagula, Feb 23 2012

			-3/x^7 - 2 + 3*x -3*x^8 - 4*x^15 + 3*x^16 - 3*x^23 - 3*x^24 - 4*x^30 + ...

Cf. A207944, A080054, A142724.

Table[SeriesCoefficient[
  Series[(1 + 2*Product[1 + x^(8*i - 1), {i, 1, Infinity}])/(-1 +
      Product[(1 - x^(8*i - 1)), {i, 1, Infinity}]), {x, 0, 100}],
  n], {n, 0, 100}]

cp's OEIS Frontend

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

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A208150 Expansion of (1 + 2Product_{i>=1} (1 + x^(8i - 1)))/(-1 + Product_{i>=1} (1 - x^(8*i - 1))).

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cp's OEIS Frontend

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

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A208150 Expansion of (1 + 2*Product_{i>=1} (1 + x^(8*i - 1)))/(-1 + Product_{i>=1} (1 - x^(8*i - 1))).

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

A208150 Expansion of (1 + 2Product_{i>=1} (1 + x^(8i - 1)))/(-1 + Product_{i>=1} (1 - x^(8*i - 1))).