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A335730
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a(n) is the number of smallest parts in the overpartitions of n having odd smallest part.
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2
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2, 4, 12, 20, 40, 72, 124, 200, 330, 520, 804, 1224, 1832, 2704, 3960, 5704, 8144, 11532, 16164, 22480, 31056, 42568, 57972, 78480, 105610, 141336, 188208, 249352, 328824, 431760, 564468, 734992, 953424, 1232144, 1586760, 2036580, 2605352, 3322584, 4224624, 5355920
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: (Product_{k>=1} (1+q^k)/(1-q^k))*(Sum_{n>=1} 2*n*q^n/(1-q^(2*n)) + Sum_{n=-oo..oo, n<>0} 4*(-1)^n*q^(n^2+n)*(1+q^(2*n)+q^(3*n))/((1-q^(2*n))*(1-q^(4*n)))).
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EXAMPLE
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There are 14 overpartitions of 4: [4], [4'], [3,1], [3,1'], [3',1], [3',1'], [2,2], [2',2], [2,1,1], [2,1',1], [2',1,1], [2',1',1], [1,1,1,1], [1',1,1,1], and so a(4) = 20.
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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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