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A055659
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Number of (2,n)-partitions of a chain of length n^3.
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2
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0, 15, 253, 1653, 6786, 21115, 54615, 123753, 253828, 481671, 858705, 1454365, 2359878, 3692403, 5599531, 8264145, 11909640, 16805503, 23273253, 31692741, 42508810, 56238315, 73477503, 94909753, 121313676, 153571575, 192678265
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OFFSET
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1,2
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COMMENTS
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a (k,n)-partition of a chain C is a chain of k intervals of C of length n.
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LINKS
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FORMULA
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a(n) = (1/2)*(n-1)*(n^2+n-1)*(n^3-2*n+2).
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EXAMPLE
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a(2)=15 because in the linearly ordered set {1,..,8} we can choose in 15 ways 2 successive blocks of 2 consecutive elements.
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PROG
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(Magma) [(1/2) *(n-1)*(n^2+n-1)*(n^3-2*n+2): n in [1..35]]; // Vincenzo Librandi, Jun 30 2011
(PARI) a(n) = (n-1)*(n^2+n-1)*(n^3-2*n+2)/2; \\ Altug Alkan, Oct 04 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), Jun 07 2000
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STATUS
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approved
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