A261766 a(n) is the number of partial derangements of an n-set with at least one orbit of size exactly n.

1, 0, 3, 8, 30, 144, 840, 5760, 45360, 403200, 3991680, 43545600, 518918400, 6706022400, 93405312000, 1394852659200, 22230464256000, 376610217984000, 6758061133824000, 128047474114560000, 2554547108585472000, 53523844179886080000, 1175091669949317120000

Offset

0,3

References

A. Laradji and A. Umar, On the number of subpermutations with fixed orbit size, Ars Combinatoria, 109 (2013), 447-460.

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = A261765(n,n) - A261765(n,n-1) for n>0, a(0)=1.

Example

a(3) = 8 because there are 8 partial derangements on {1,2,3} with at least one orbit of size 3 namely: (1,2) --> (2,3), (1,2)  --> (3,1), (1,3)  --> (2,1), (1,3) --> (3,2), (2,3)  --> (3,1), (2,3)  --> (1,2), (1,2,3) --> (2,3,1), (1,2,3)  --> (3,1,2).

Crossrefs

Cf. A001048, A059171, A157400, A261762, A261763, A261764, A261765, A261767.

Sequence in context: A066764 A349426 A059171 * A078619 A274934 A066304

Adjacent sequences: A261763 A261764 A261765 * A261767 A261768 A261769

Keyword

nonn

Author

Samira Stitou, Sep 21 2015

Extensions

More terms from Alois P. Heinz, Nov 04 2015

Status

approved