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A213048
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Number of preferential arrangements of n labeled elements with repetitions allowed.
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0
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1, 1, 5, 31, 229, 1981, 19775, 224589, 2864901, 40591255, 632760105, 10765616885, 198543617119, 3945765358653, 84070841065937, 1911864488674531, 46222718892288645, 1183919151676806177, 32025836905529003471, 912372909851608715945, 27304698509111141688969
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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a(n) = Sum_{k=1..n} C(n+k-1,k)*a(n-k) for n>0, a(0) = 1.
a(n) = Sum_c(n) C(n+k1-1,k1) C(n-k1+k2-1,k2) C(n-k1-k2+k3-1,k3) ..., where Sum_c(n) denotes the sum over all compositions (ordered partitions) of n = k1 + k2 + ... .
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EXAMPLE
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For n=2 the a(2) = 5 solutions are (1,2), (1|2), (2|1), (1|1), (2|2).
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MAPLE
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a:= proc(n) option remember;
`if`(n=0, 1, add (binomial(n+k-1, k)*a(n-k), k=1..n))
end:
seq (a(n), n=0..25);
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CROSSREFS
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Cf. A000670.
Sequence in context: A001910 A052773 A062147 * A069321 A211179 A177797
Adjacent sequences: A213045 A213046 A213047 * A213049 A213050 A213051
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KEYWORD
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nonn
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AUTHOR
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Thomas Wieder, Jun 03 2012
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STATUS
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approved
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