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A335724
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a(n) is the number of smallest parts in the overpartitions of n.
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2
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2, 6, 12, 26, 44, 84, 136, 230, 366, 580, 884, 1356, 2012, 2968, 4320, 6226, 8856, 12522, 17508, 24324, 33528, 45892, 62392, 84372, 113374, 151548, 201552, 266752, 351380, 460920, 601992, 783158, 1014984, 1310600, 1686408, 2162814, 2764748, 3523324, 4476720, 5671748
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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.: 2*(Product_{k>=1} (1+q^k)/(1-q^k))*Sum_{n>=1} (q^n*Product_{j=1..n}(1-q^j))/((1-q^n)^2*Product_{j=1..n}(1+q^j)).
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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) = 26.
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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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