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Search: id:A063834
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| A063834 |
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Twice partitioned numbers: the number of ways a number can be partitioned in (not necessarily different) parts, and each part again so partitioned. |
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4
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| 1, 3, 6, 15, 28, 66, 122, 266, 503, 1027, 1913, 3874, 7099, 13799, 25501, 48508, 88295, 165942, 299649, 554545, 997281, 1817984, 3245430, 5875438, 10410768, 18635587, 32885735, 58399350, 102381103, 180634057, 314957425, 551857780
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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These are different from plane partitions.
For ordered partitions of partitions see A055887 which may be computed from A036036 and A048996. - Alford Arnold (Alford1940(AT)aol.com), May 19 2006
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..500
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FORMULA
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G.f.: 1/Product_{k>0} (1-A000041(k)*x^k). a(n) = 1/n*Sum_{k=1..n} b(k)*a(n-k), a(0) = 1, where b(k) = Sum_{d|k} d*A000041(d)^(k/d). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 19 2003
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EXAMPLE
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If n=6, a possible first partitioning is (3+3), resulting in the following second partitionings: ((3),(3)), ((3),(2+1)), ((3),(1+1+1)), ((2+1),(3)), ((2+1),(2+1)), ((2+1),(1+1+1)), ((1+1+1),(3)), ((1+1+1),(2+1)), ((1+1+1),(1+1+1))
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MATHEMATICA
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Table[Plus@@Apply[Times, Partitions[i]/.i_Integer:>PartitionsP[i], 2], {i, 36}]
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CROSSREFS
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Cf. A063835.
Cf. A036036, A048996, A055887.
Sequence in context: A103529 A034953 A086737 this_sequence A139117 A066708 A034464
Adjacent sequences: A063831 A063832 A063833 this_sequence A063835 A063836 A063837
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KEYWORD
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nonn,nice
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 21 2001
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