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A364324
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a(n) = n!*tribonacci(n+2).
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5
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1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120, 994291200, 20118067200, 444034483200, 10617070464000, 273391121203200, 7542665754624000, 221969877921792000, 6940528784437248000, 229781192298577920000, 8030036368187817984000, 295390797322766745600000
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of ways to partition [n] into blocks of size at most 3, order the blocks, and order the elements within each block.
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LINKS
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FORMULA
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E.g.f.: 1/(1-x-x^2-x^3).
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EXAMPLE
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a(5) = 1560 since the number of ways to partition [5] into blocks of size at most 3, order the blocks, and order the elements within each block are the following:
1) 1,2,3,4,5: 120 ordered blocks; 120 ways;
2) 12,3,4,5: 240 ordered blocks; 480 ways;
3) 12,34,5: 90 ordered blocks; 360 ways;
4) 123,45: 20 ordered blocks; 240 ways;
5) 123,4,5: 60 ordered blocks; 360 ways.
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-i)*binomial(n, i)*i!, i=1..min(n, 3)))
end:
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MATHEMATICA
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With[{m = 21}, Range[0, m - 1]! * LinearRecurrence[{1, 1, 1}, {1, 1, 2}, m]] (* Amiram Eldar, Jul 28 2023 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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