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 A231536 Triangular array read by rows.  T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} whose functional digraph has exactly k nodes such that no nonrecurrent element is mapped into it.  n >= 1, 1 <= k <= n. 0
 1, 2, 2, 6, 15, 6, 24, 108, 100, 24, 120, 840, 1340, 705, 120, 720, 7200, 17400, 15150, 5466, 720, 5040, 68040, 231000, 296100, 171402, 46921, 5040, 40320, 705600, 3198720, 5644800, 4687536, 2015272, 444648, 40320, 362880, 7983360, 46569600, 108168480, 121144464, 73191888, 25011576, 4625361, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA E.g.f.: 1/(1 - A(x,y)) where A(x,y) is the e.g.f. for A055302. EXAMPLE T(3,3) = 6 because we have: (1,2,3),(2,1,3),(3,2,1),(1,3,2),(2,3,1),(3,1,2).  In these 6 functions represented as a word there are 3 (all) elements with zero nonrecurrent elements mapped to them. 1, 2, 2, 6, 15, 6, 24, 108, 100, 24, 120, 840, 1340, 705, 120, 720, 7200, 17400, 15150, 5466, 720 MATHEMATICA nn=6; Map[Select[#, #>0&]&, Drop[Range[0, nn]!CoefficientList[Series[1/(1- (-x+x y-ProductLog[-Exp[x (-1+y)] x])), {x, 0, nn}], {x, y}], 1]]//Grid CROSSREFS Row sums give: A000312. Column k=1 and main diagonal give: A000142. Sequence in context: A142471 A323233 A071208 * A216242 A330798 A260687 Adjacent sequences:  A231533 A231534 A231535 * A231537 A231538 A231539 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Nov 10 2013 STATUS approved

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Last modified August 14 13:43 EDT 2022. Contains 356117 sequences. (Running on oeis4.)