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A246191 Number of endofunctions on [n] where the smallest cycle length equals 4. 2
6, 120, 2160, 41160, 861420, 19949328, 510320160, 14348862000, 440879024520, 14716697990280, 530761366078944, 20577610843203960, 853717568817968400, 37746072677473752480, 1771994498414094109440, 88032162789004128733152, 4614300279345812506938720 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..200

FORMULA

a(n) ~ (exp(-11/6) - exp(-25/12)) * 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, 4) -A(n, 5):

seq(a(n), n=4..25);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_] := b[n, i] = If[n==0, 1, If[i>n, 0, Sum[(i - 1)!^j multinomial[n, Join[{n - i*j}, Table[i, {j}]]]/j! b[n - i*j, i + 1], {j, 0, n/i}]]];

A[n_, k_] := Sum[Binomial[n - 1, j - 1] n^(n - j) b[j, k], {j, 0, n}];

a[n_] := A[n, 4] - A[n, 5];

a /@ Range[4, 25] (* Jean-Fran├žois Alcover, Dec 28 2020, after Alois P. Heinz *)

CROSSREFS

Column k=4 of A246049.

Sequence in context: A026337 A223629 A065888 * A246611 A185757 A075844

Adjacent sequences:  A246188 A246189 A246190 * A246192 A246193 A246194

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 18 2014

STATUS

approved

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Last modified May 25 22:51 EDT 2022. Contains 354073 sequences. (Running on oeis4.)