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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, 3934, 4496, 5144, 5878, 6698, 7638, 8698, 9886
OFFSET
0,4
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
Shi-Chao Chen, 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
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] (* fixed by Vaclav Kotesovec, Apr 13 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Feb 21 2012
STATUS
approved