A261767 Triangle read by rows: T(n,k) is the number of subpermutations of an n-set, whose orbits are each of size at most k with at least one orbit of size exactly k.

1, 1, 1, 1, 3, 3, 1, 7, 18, 8, 1, 15, 99, 64, 30, 1, 31, 510, 560, 300, 144, 1, 63, 2745, 4800, 3150, 1728, 840

Offset

0,5

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..27.

Formula

T(n, k) = A261763(n, k) - A261763(n, k-1), T(n, n) = A261766(n) for all n not equal to 1 and T(1, 1) = 1.

Example

T(3, 2) = 18 because there are 18 subpermutations on {1,2,3} whose orbits are each of size at most 2 with at least one orbit of size exactly 2, namely: (1 2 --> 2 1), (1 3 --> 3 1), (2 3 --> 3 2), (123 --> 213), (123 --> 321), (123 --> 132); (1-->2), (1-->3), (2-->1), (2-->3), (3-->1), (3-->2); (13-->23), (12-->32), (23-->13), (32-->33), (23-->21), (13-->12).
Triangle starts:
1;
1, 1;
1, 3, 3;
1, 7, 18, 8;
1, 15, 99, 64, 30;
1, 31, 510, 560, 300, 144;
...

Crossrefs

Cf. A261762, A261763, A261764, A261765, A261766, A261767.

Row sums give A002720.

Sequence in context: A118408 A079268 A102316 * A355315 A300620 A133709

Adjacent sequences: A261764 A261765 A261766 * A261768 A261769 A261770

Keyword

nonn,tabl,more

Author

Samira Stitou, Sep 21 2015

Status

approved