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

Author

Samira Stitou, Sep 21 2015

Keywords

• nonn

Examples

			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).
		

References

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

Crossrefs

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

Formula

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

Extensions

More terms from Alois P. Heinz, Nov 04 2015