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

1,2

Links

Alois P. Heinz, Rows n = 1..20, flattened

Wikipedia, Permutation

Example

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;
  ...

Crossrefs

Column k=1 gives A285382.

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

Row sums give A000142 * A000217 = A180119.

Cf. A285793, A286232.

Sequence in context: A162259 A077195 A038243 * A218016 A193685 A174358

Adjacent sequences: A286228 A286229 A286230 * A286232 A286233 A286234

Keyword

nonn,tabl

Author

Alois P. Heinz, May 04 2017

Status

approved