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A246190 Number of endofunctions on [n] where the smallest cycle length equals 3. 2
2, 24, 300, 4360, 74130, 1456224, 32562152, 817596000, 22785399450, 697951656160, 23306666102148, 842567564800416, 32781106696806650, 1365579024023558400, 60639189588419033040, 2859165143013913590016, 142651621238828972159538, 7508140027468431374563200 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..200

FORMULA

a(n) ~ (exp(-3/2) - exp(-11/6)) * 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, 3) -A(n, 4):

seq(a(n), n=3..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, 3] - A[n, 4];

a /@ Range[3, 25] (* Jean-Fran├žois Alcover, Dec 28 2020, after Alois P. Heinz *)

CROSSREFS

Column k=3 of A246049.

Sequence in context: A135389 A336310 A065513 * A246610 A119491 A001864

Adjacent sequences:  A246187 A246188 A246189 * A246191 A246192 A246193

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 18 2014

STATUS

approved

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Last modified May 16 16:43 EDT 2022. Contains 353707 sequences. (Running on oeis4.)