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Search: id:A096911
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| A096911 |
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Number of partitions of n into distinct parts with exactly one even part. |
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+0
3
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| 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 15, 18, 20, 23, 26, 30, 34, 38, 43, 49, 55, 61, 69, 77, 86, 95, 106, 118, 131, 144, 160, 177, 195, 214, 236, 260, 285, 312, 342, 375, 410, 447, 488, 534, 581, 632, 688, 749, 813, 882, 957, 1039, 1125, 1217, 1317, 1426
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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G.f.: x^2/(1-x^2)*Product(1+x^(2*i+1), i=0..infinity). More generally, g.f. for number of partitions of n into distinct parts with exactly k even parts is x^(k*(k+1))/Product(1-x^(2*i), i=1..k)*Product(1+x^(2*i+1), i=0..infinity).
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MATHEMATICA
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Drop[ CoefficientList[ Series[x^2/(1 - x^2) * Product[1 + x^(2*i + 1), {i, 0, 70}], {x, 0, 62}], x], 1] (from Robert G. Wilson v Aug 21 2004)
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CROSSREFS
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Cf. A000700.
Sequence in context: A106244 A029023 A140952 this_sequence A143752 A145933 A120171
Adjacent sequences: A096908 A096909 A096910 this_sequence A096912 A096913 A096914
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 17 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 21 2004
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