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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)