A286231 Sum T(n,k) of the entries in the k-th last cycles of all permutations of [n]; triangle T(n,k), n>=1, 1<=k<=n, read by rows.

1, 5, 1, 25, 10, 1, 143, 79, 17, 1, 942, 634, 197, 26, 1, 7074, 5462, 2129, 417, 37, 1, 59832, 51214, 23381, 5856, 786, 50, 1, 563688, 523386, 269033, 80053, 13934, 1360, 65, 1, 5858640, 5813892, 3281206, 1111498, 232349, 29728, 2204, 82, 1

Offset: 1

Author

Alois P. Heinz, May 04 2017

Keywords

• nonn
• tabl

Examples

			T(3,2) = 10 because the sum of the entries in the second last cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 0+0+3+4+1+2 = 10.
Triangle T(n,k) begins:
       1;
       5,      1;
      25,     10,      1;
     143,     79,     17,     1;
     942,    634,    197,    26,     1;
    7074,   5462,   2129,   417,    37,    1;
   59832,  51214,  23381,  5856,   786,   50,  1;
  563688, 523386, 269033, 80053, 13934, 1360, 65, 1;
  ...
		

Links

• Alois P. Heinz, Rows n = 1..20, flattened
• Wikipedia, Permutation

Crossrefs

Column k=1 gives A285382.

Main diagonal and first lower diagonal give: A000012, A002522.

Row sums give A000142 * A000217 = A180119.

Cf. A285793, A286232.