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 A152684 a(n) is the number of top-down sequences (F_1, F_2, ..., F_n) whereas each F_i is a labeled forest on n nodes, containing i directed rooted trees. F_(i+1) is proper subset of F_i. 4
 1, 2, 18, 384, 15000, 933120, 84707280, 10569646080, 1735643790720, 362880000000000, 94121726392108800, 29658516531078758400, 11159820050604594969600, 4942478402320838374195200, 2544989406021562500000000000, 1507645899890367707813511168000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Miklos Bona, Introduction to Enumerative Combinatorics, McGraw Hill 2007, Page 276. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..100 FORMULA a(n) = n^(n-2)*(n!). EXAMPLE a(1) = 1^(1-2)*(1!) = 1. a(2) = 2^(2-2)*(2!) = 2. a(3) = 3^(3-2)*(3!) = 18. MAPLE a:= proc(n) option remember; `if`(n=1, 1, a(n-1)*(n/(n-1))^(n-3)*n^2) end: seq(a(n), n=1..20); # Alois P. Heinz, May 16 2013 MATHEMATICA Table[n^(n - 1) (n - 1)!, {n, 1, 16}] (* Geoffrey Critzer, May 10 2013 *) PROG (Magma) [Factorial(n-1)*n^(n-1): n in [1..20]]; // G. C. Greubel, Nov 28 2022 (SageMath) [factorial(n-1)*n^(n-1) for n in range(1, 21)] # G. C. Greubel, Nov 28 2022 CROSSREFS Cf. A061711, A066319, A137268. Sequence in context: A291902 A336217 A226837 * A201732 A374278 A260656 Adjacent sequences: A152681 A152682 A152683 * A152685 A152686 A152687 KEYWORD nonn AUTHOR Fabian Nedic, Dec 10 2008 STATUS approved

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Last modified August 11 01:05 EDT 2024. Contains 375059 sequences. (Running on oeis4.)