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A246192 Number of endofunctions on [n] where the smallest cycle length equals 5. 2
24, 720, 17640, 430080, 11022480, 302472576, 8937981360, 284552040960, 9743091569640, 357820740076800, 14051646110285784, 588177615908413440, 26161789829441054880, 1232890909824506204160, 61387038018996808785120, 3221070809733138102829056 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..200

FORMULA

a(n) ~ (exp(-25/12) - exp(-137/60)) * 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, 5) -A(n, 6):

seq(a(n), n=5..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, 5] - A[n, 6];

a /@ Range[5, 25] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A246049.

Sequence in context: A184274 A093456 A189412 * A246612 A289635 A105187

Adjacent sequences:  A246189 A246190 A246191 * A246193 A246194 A246195

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 18 2014

STATUS

approved

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Last modified December 6 17:58 EST 2021. Contains 349567 sequences. (Running on oeis4.)