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A261766 a(n) is the number of partial derangements of an n-set with at least one orbit of size exactly n. 5
1, 0, 3, 8, 30, 144, 840, 5760, 45360, 403200, 3991680, 43545600, 518918400, 6706022400, 93405312000, 1394852659200, 22230464256000, 376610217984000, 6758061133824000, 128047474114560000, 2554547108585472000, 53523844179886080000, 1175091669949317120000 (list; graph; refs; listen; history; text; internal format)
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: A009123 A066764 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

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Last modified February 21 02:19 EST 2018. Contains 299388 sequences. (Running on oeis4.)