A285233 Number of entries in the fifth cycles of all permutations of [n].

1, 17, 221, 2724, 34009, 441383, 6020276, 86673088, 1318681308, 21194234508, 359421505224, 6421154849208, 120637782989568, 2379195625677696, 49167226489281408, 1062833010282628992, 23992442301958329600, 564697104190192569600, 13836823816466433139200

Offset

5,2

Comments

Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

Links

Alois P. Heinz, Table of n, a(n) for n = 5..449

Wikipedia, Permutation

Formula

a(n) = A185105(n,5).

a(n) ~ n!*n/32. - Vaclav Kotesovec, Apr 25 2017

Maple

a:= proc(n) option remember; `if`(n<6, [0$5, 1][n+1],
      ((4*(n^3-9*n^2+24*n-19))*a(n-1)-(6*n^4-72*n^3+
       307*n^2-547*n+334)*a(n-2)+(4*n^5-64*n^4+398*n^3
      -1191*n^2+1683*n-862)*a(n-3)-(n-4)^5*(n-1)*a(n-4))
      /((n-2)*(n-5)))
    end:
seq(a(n), n=5..25);

Mathematica

a[3] = a[4] = 0; a[5] = 1; a[6] = 17; a[n_] := a[n] = ((4(n^3 - 9n^2 + 24n - 19)) a[n-1] - (6n^4 - 72n^3 + 307n^2 - 547n + 334) a[n-2] + (4n^5 - 64n^4 + 398n^3 - 1191n^2 + 1683n - 862) a[n-3] - (n-4)^5 (n-1) a[n-4]) / ((n - 2)(n - 5));
Table[a[n], {n, 5, 25}] (* Jean-François Alcover, Jun 01 2018, from Maple *)

Crossrefs

Column k=5 of A185105.

Sequence in context: A322538 A016238 A016181 * A063043 A016174 A016281

Adjacent sequences: A285230 A285231 A285232 * A285234 A285235 A285236

Keyword

nonn

Author

Alois P. Heinz, Apr 15 2017

Status

approved