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Search: id:A066185
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| A066185 |
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Sum of the first moments of all partitions of n. |
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+0
4
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| 0, 1, 4, 12, 26, 57, 103, 191, 320, 537, 843, 1342, 2015, 3048, 4457, 6509, 9250, 13170, 18316, 25483, 34853, 47556, 64017, 86063, 114285, 151462, 198871, 260426, 338275, 438437, 564131, 724202, 924108, 1176201, 1489237, 1881273, 2365079
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The first element of each partition is given weight 0.
Consider the partitions of n, e.g. n=5. For each partition sum T(e-1), and sum all these. e.g. 5 -> T(4)=10, 41 -> T(3)+T(0)=6, 32 -> T(2)+T(1)=4, 311 -> T(2)+T(0)+T(0)=3, 221 -> T(1)+T(1)+T(0)=2, 21111 ->1 and 11111 ->0. Summing, 10+6+4+3+2+1+0 = 26 as desired. - Jon Perry (perry(AT)globalnet.co.uk), Dec 12 2003
Sum of zero-based moments of ordered partitions (see A066185). - Jon Perry (perry(AT)globalnet.co.uk), Dec 12 2003
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FORMULA
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a(n) = 1/2*(A066183(n) - A066186(n)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 23 2003
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EXAMPLE
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a(3)=4 because the first moments of all partitions of 3 are {3}.{0},{2,1}.{0,1} and {1,1,1}.{0,1,2}, resulting in 0,1,3; summing to 4.
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MATHEMATICA
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(* First do <<DiscreteMath`Combinatorica` *) Table[ Plus@@ Map[ #.Range[ 0, -1+Length[ # ] ]&, Partitions[ n ] ], {n, 40} ]
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CROSSREFS
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Cf. A066184.
Cf. A000337.
Cf. A001788.
Cf. A066185.
Sequence in context: A008159 A057307 A009844 this_sequence A008107 A057306 A047732
Adjacent sequences: A066182 A066183 A066184 this_sequence A066186 A066187 A066188
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KEYWORD
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easy,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 15 2001
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