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A207944 Expansion of Product_{i>=1} (1 + x^(2*i + 1))/(1 - x^(2*i + 1)). 2
1, 0, 0, 2, 0, 2, 2, 2, 4, 4, 6, 6, 10, 10, 14, 18, 20, 26, 32, 38, 46, 58, 66, 82, 98, 116, 138, 166, 194, 230, 274, 318, 376, 442, 514, 602, 704, 814, 950, 1102, 1274, 1474, 1706, 1962, 2262, 2606, 2986, 3430 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Mathematica gives the closed form:k[x_] = Product[(1 + x^(2*i + 1))/(1 - x^(2*i + 1)), {i, 1, Infinity}] as

-(((-1 + x) QPochhammer[-x, x^2])/((1 + x) QPochhammer[x, x^2]))

REFERENCES

George E. Andrews, Number Theory, Dover Publications, N.Y., 1971, 164-165.

Chen, Shi-Chao. On the number of overpartitions into odd parts. Discrete Math. 325 (2014), 32--37. MR3181230. The g.f. occurs on page 32, by accident (the product there should really start at n=0, not 1, in order to give A080054!). - N. J. A. Sloane, Apr 24 2014

Samuel I. Goldberg, Curvature and Homology, Dover, New York, 1998, 144.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

a(n) ~ exp(sqrt(n/2)*Pi) * Pi / (2^(19/4) * n^(5/4)). - Vaclav Kotesovec, Apr 13 2017

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k + 1))/(1 - x^(2*k + 1)), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A015128, A080054, A142724.

Sequence in context: A199123 A325589 A291308 * A063088 A101276 A103863

Adjacent sequences:  A207941 A207942 A207943 * A207945 A207946 A207947

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Feb 21 2012

EXTENSIONS

Mathematica program fixed by Vaclav Kotesovec, Apr 13 2017

STATUS

approved

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Last modified May 21 00:57 EDT 2019. Contains 323429 sequences. (Running on oeis4.)