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 A364324 a(n) = n!*tribonacci(n+2). 5
 1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120, 994291200, 20118067200, 444034483200, 10617070464000, 273391121203200, 7542665754624000, 221969877921792000, 6940528784437248000, 229781192298577920000, 8030036368187817984000, 295390797322766745600000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS Table of n, a(n) for n=0..20. FORMULA E.g.f.: 1/(1-x-x^2-x^3). a(n) = A000142(n) * A000073(n+2). EXAMPLE 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. MAPLE a:= proc(n) option remember; `if`(n=0, 1, add( a(n-i)*binomial(n, i)*i!, i=1..min(n, 3))) end: seq(a(n), n=0..20); # Alois P. Heinz, Jul 18 2023 MATHEMATICA With[{m = 21}, Range[0, m - 1]! * LinearRecurrence[{1, 1, 1}, {1, 1, 2}, m]] (* Amiram Eldar, Jul 28 2023 *) CROSSREFS Cf. A000073, A000142, A002866, A005442, A189886. Sequence in context: A212277 A246423 A188913 * A052685 A221088 A365225 Adjacent sequences: A364321 A364322 A364323 * A364325 A364326 A364327 KEYWORD nonn AUTHOR Enrique Navarrete, Jul 18 2023 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)