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 A219706 Total number of nonrecurrent elements in all functions f:{1,2,...,n}->{1,2,...,n}. 2
 0, 0, 2, 30, 456, 7780, 150480, 3279234, 79775360, 2146962024, 63397843200, 2039301671110, 71007167075328, 2661561062560140, 106874954684266496, 4577827118698118250, 208369657238965616640, 10044458122057793060176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS x in {1,2,...,n} is a recurrent element if there is some k such that f^k(x) = x where f^k(x) denotes iterated functional composition. In other words, a recurrent element is in a cycle of the functional digraph. An element that is not recurrent is a nonrecurrent element. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..385 FORMULA E.g.f.: T(x)^2/(1-T(x))^3  where T(x) is the e.g.f. for A000169. a(n) = Sum_{k=1..n-1} A219694{n,k)*k. a(n) = n^(n+1) - A063169(n). MAPLE b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->p+       [0, p[1]*j])((j-1)!*b(n-j)*binomial(n-1, j-1)), j=1..n))     end: a:= n-> (p-> n*p[1]-p[2])(add(b(j)*n^(n-j)          *binomial(n-1, j-1), j=0..n)): seq(a(n), n=0..25);  # Alois P. Heinz, May 22 2016 MATHEMATICA nn=20; f[list_] := Select[list, #>0&]; t=Sum[n^(n-1)x^n y^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[D[1/(1-x Exp[t]), y]/.y->1, {x, 0, nn}], x] CROSSREFS Sequence in context: A285298 A134362 A296980 * A318477 A219869 A072976 Adjacent sequences:  A219703 A219704 A219705 * A219707 A219708 A219709 KEYWORD nonn AUTHOR Geoffrey Critzer, Nov 25 2012 STATUS approved

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Last modified July 25 16:03 EDT 2021. Contains 346291 sequences. (Running on oeis4.)