A211880 Number of permutations of n elements with no fixed points and largest cycle of length 3.

0, 0, 0, 2, 0, 20, 40, 210, 1120, 4760, 25200, 157850, 800800, 5345340, 35035000, 222472250, 1648046400, 12000388400, 88529240800, 720929459250, 5786188408000, 48072795270500, 424300329453000, 3731123025279650, 34083741984292000, 323768324084205000

Offset

0,4

Comments

a(n) = A055814(n) - A123023(n). - Vaclav Kotesovec, Oct 09 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Formula

E.g.f.: (exp(x^3/3)-1) * exp(x^2/2).

Recurrence: (n-3)*a(n) = (n-1)*(2*n-5)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*a(n-4) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-5). - Vaclav Kotesovec, Oct 09 2013

Example

a(3) = 2: (2,3,1), (3,1,2).

Maple

egf:= (exp(x^3/3)-1)*exp(x^2/2):
a:= n-> n! *coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..30);

Mathematica

A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1,
     Sum[Product[n - i, {i, 1, j - 1}] A[n - j, k], {j, 2, k}]]];
T[n_, k_] := A[n, k] - If[k == 0, 0, A[n, k - 1]];
a[n_] := T[n, 3];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Sep 03 2021, after Alois P. Heinz in A211871 *)

Crossrefs

Column k=3 of A211871.

Cf. A055814, A123023.

Sequence in context: A139003 A264881 A280622 * A365862 A209868 A182661

Adjacent sequences: A211877 A211878 A211879 * A211881 A211882 A211883

Keyword

nonn

Author

Alois P. Heinz, Feb 13 2013

Status

approved