A263757 Triangle read by rows: T(n,k) (n>=1, 0<=k<n) is the number of permutations of n with maximal difference k between elements in the same cycle.

1, 1, 1, 1, 2, 3, 1, 4, 7, 12, 1, 7, 17, 35, 60, 1, 12, 44, 93, 210, 360, 1, 20, 103, 275, 651, 1470, 2520, 1, 33, 234, 877, 2047, 5208, 11760, 20160, 1, 54, 533, 2544, 7173, 18423, 46872, 105840, 181440, 1, 88, 1196, 7135, 27085, 67545, 184230, 468720, 1058400, 1814400

Offset

1,5

Comments

Row sums give A000142, n >= 1.

Main diagonal gives A001710. - Alois P. Heinz, Sep 20 2016

Links

Alois P. Heinz, Rows n = 1..15, flattened

FindStat - Combinatorial Statistic Finder, Maximum difference of elements in cycles.

Formula

T(n,k) = A276837(n,k+1) - A276837(n,k). - Alois P. Heinz, Sep 20 2016

Example

Triangle begins:
  1;
  1,  1;
  1,  2,  3;
  1,  4,  7, 12;
  1,  7, 17, 35,  60;
  1, 12, 44, 93, 210, 360;
  ...

Crossrefs

Cf. A000071, A000142, A001710, A276727, A276837, A276974, A277031.

Sequence in context: A171083 A364602 A258579 * A021436 A179738 A377307

Adjacent sequences: A263754 A263755 A263756 * A263758 A263759 A263760

Keyword

nonn,tabl

Author

Christian Stump, Oct 25 2015

Extensions

More terms (rows n=7-10) from Alois P. Heinz, Sep 20 2016

Status

approved