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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: A060042 A217855 A134362 * A219869 A072976 A143414

Adjacent sequences:  A219703 A219704 A219705 * A219707 A219708 A219709

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Nov 25 2012

STATUS

approved

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Last modified December 5 21:40 EST 2016. Contains 278771 sequences.