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A261037
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The number of overpartitions of n with restricted odd differences and smallest part both odd and overlined.
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0
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1, 1, 3, 4, 7, 10, 17, 23, 36, 48, 73, 96, 140, 182, 259, 334, 463, 592, 806, 1024, 1370, 1728, 2281, 2860, 3727, 4646, 5991, 7430, 9487, 11706, 14822, 18205, 22870, 27966, 34890, 42492, 52670, 63896, 78743, 95178, 116659, 140516, 171380, 205750
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OFFSET
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1,3
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COMMENTS
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The number of overpartitions of n such that: (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) the smallest part of the overpartition is both odd and overlined.
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LINKS
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FORMULA
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G.f.: 1 + 3*Sum_{n >= 1} a(n)q^n = Product_{n >= 1} (1-q^(3*n))/((1-q^n)*(1-q^(2*n)) * (1 + 2*Sum_{n >= 1} q^(n(n+1)/2)*(1-q^2)(1-q^4)...(1-q^(2*n-2))*(1-q^n)/((1-q^3)(1-q^6)...(1-q^(3*n))).
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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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