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 A209290 Number of elements whose preimage is the empty set summed over all functions f:{1,2,...,n}->{1,2,...,n}. 1
 0, 0, 2, 24, 324, 5120, 93750, 1959552, 46118408, 1207959552, 34867844010, 1100000000000, 37661140520652, 1390911669927936, 55123269399790046, 2333521433367183360, 105094533691406250000, 5017514388048998039552, 253135520137219049838162, 13456471561751415850795008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)/n^n is the expected value of the number of such elements which approaches n/e as n gets large. a(n) = Sum_{k=1..n} A219859(n,k)*k. a(n) = 2 * A109391(n-1) = 2 * A000217(n-1) * A000312(n-1) for n>0. a(n-1) is the number of length-n words of n-1 letters where adjacent letters are distinct, see example. - Joerg Arndt, Jun 10 2013 LINKS FORMULA a(n) = n*(n - 1)^n. EXAMPLE From Joerg Arndt, Jun 10 2013: (Start) There are a(4-1)=a(3)=24 length-4 words of 3 letters (0,1,2) where adjacent letters are distinct: 01:  [ 0 1 0 1 ] 02:  [ 0 1 0 2 ] 03:  [ 0 1 2 0 ] 04:  [ 0 1 2 1 ] 05:  [ 0 2 0 1 ] 06:  [ 0 2 0 2 ] 07:  [ 0 2 1 0 ] 08:  [ 0 2 1 2 ] 09:  [ 1 0 1 0 ] 10:  [ 1 0 1 2 ] 11:  [ 1 0 2 0 ] 12:  [ 1 0 2 1 ] 13:  [ 1 2 0 1 ] 14:  [ 1 2 0 2 ] 15:  [ 1 2 1 0 ] 16:  [ 1 2 1 2 ] 17:  [ 2 0 1 0 ] 18:  [ 2 0 1 2 ] 19:  [ 2 0 2 0 ] 20:  [ 2 0 2 1 ] 21:  [ 2 1 0 1 ] 22:  [ 2 1 0 2 ] 23:  [ 2 1 2 0 ] 24:  [ 2 1 2 1 ] (End) MATHEMATICA Table[n (n-1)^n, {n, 0, 20}] PROG (PARI) a(n) = n*(n-1)^n; \\ Michel Marcus, Aug 22 2017 CROSSREFS Sequence in context: A001864 A099045 A181174 * A081065 A043699 A220317 Adjacent sequences:  A209287 A209288 A209289 * A209291 A209292 A209293 KEYWORD nonn,easy AUTHOR Geoffrey Critzer, Jan 16 2013 STATUS approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)