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A246189 Number of endofunctions on [n] where the smallest cycle length equals 2. 2
1, 6, 51, 580, 8265, 141246, 2810437, 63748728, 1622579985, 45775778950, 1417347491241, 47776074289164, 1741386177576409, 68238497945688630, 2860625245955274225, 127736893134458097136, 6052712065187733972513, 303322427195785592735502, 16028016368907840953165425 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..200

FORMULA

a(n) ~ (exp(-1) - exp(-3/2)) * n^n. - Vaclav Kotesovec, Aug 21 2014

MAPLE

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,

      add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

      b(n-i*j, i+1), j=0..n/i)))

    end:

A:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j, k), j=0..n):

a:= n-> A(n, 2) -A(n, 3):

seq(a(n), n=2..25);

CROSSREFS

Column k=2 of A246049.

Sequence in context: A000405 A113352 A063169 * A293128 A304185 A215003

Adjacent sequences:  A246186 A246187 A246188 * A246190 A246191 A246192

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 18 2014

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)