A285234 Number of entries in the sixth cycles of all permutations of [n].

1, 23, 382, 5780, 86029, 1301673, 20338679, 330737236, 5618265376, 99849949772, 1857170751804, 36135886878072, 734947859916792, 15608257104179952, 345724111468700496, 7977315239656638912, 191516062334747746752, 4778050475554642998144, 123731984754223222096512

Offset

6,2

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 = 6..449

Wikipedia, Permutation

Formula

a(n) = A185105(n,6).

a(n) ~ n!*n/64. - Vaclav Kotesovec, Apr 25 2017

Maple

a:= proc(n) option remember; `if`(n<7, [0$6, 1][n+1],
      ((5*n^3-58*n^2+207*n-230)*a(n-1)-(10*n^4-152*n^3
       +835*n^2-1973*n+1690)*a(n-2)+(n-4)*(10*n^4
       -158*n^3+909*n^2-2251*n+2000)*a(n-3)-(5*n^6
       -127*n^5+1330*n^4-7335*n^3+22396*n^2-35717*n
       +23058)*a(n-4)+(n-5)^6*(n-2)*a(n-5))/((n-3)*(n-6)))
    end:
seq(a(n), n=6..25);

Mathematica

b[n_, i_] := b[n, i] = Expand[If[n==0, 1, Sum[Function[p, p + Coefficient[ p, x, 0]*j*x^i][b[n-j, i+1]]*Binomial[n-1, j-1]*(j-1)!, {j, 1, n}]]];
a[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, 1]][[6]];
Table[a[n], {n, 6, 25}] (* Jean-François Alcover, Jun 01 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A185105.

Sequence in context: A016325 A016324 A264321 * A046493 A014926 A353117

Adjacent sequences: A285231 A285232 A285233 * A285235 A285236 A285237

Keyword

nonn

Author

Alois P. Heinz, Apr 15 2017

Status

approved