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A305102
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G.f.: Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} (1+x^k)/(1-x^k).
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8
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0, 1, 4, 10, 23, 46, 88, 158, 274, 459, 748, 1190, 1858, 2846, 4292, 6384, 9373, 13602, 19536, 27782, 39158, 54740, 75928, 104562, 143036, 194423, 262704, 352988, 471778, 627382, 830352, 1093994, 1435132, 1874920, 2439832, 3163020, 4085825, 5259602, 6748136
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of non-overlined parts in all overpartitions of n. - Joerg Arndt, Jun 18 2020
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(n)) * (2*gamma + log(4*n/Pi^2)) / (8*Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620.
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Sum[x^k/(1-x^k), {k, 1, nmax}] * Product[(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
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PROG
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(PARI) my(N=44, q='q+O('q^N)); Vec( prod(k=1, N, (1+q^k)/(1-q^k)) * sum(k=1, N, 1*q^k/(1-q^k)) ) \\ Joerg Arndt, Jun 18 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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