A344901 Triangle read by rows: T(n,k) is the number of permutations of length n that have k same elements at the same positions with its inverse permutation for 0 <= k <= n.

1, 0, 1, 0, 0, 2, 2, 0, 0, 4, 6, 8, 0, 0, 10, 24, 30, 40, 0, 0, 26, 160, 144, 180, 160, 0, 0, 76, 1140, 1120, 1008, 840, 700, 0, 0, 232, 8988, 9120, 8960, 5376, 4200, 2912, 0, 0, 764, 80864, 80892, 82080, 53760, 30240, 19656, 12768, 0, 0, 2620, 809856, 808640, 808920, 547200, 336000, 157248, 95760, 55680, 0, 0, 9496

Offset

0,6

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = binomial(n,k)*A000085(k)*A038205(n-k).

Example

Triangle T(n,k) begins:
     1;
     0,    1;
     0,    0,    2;
     2,    0,    0,    4;
     6,    8,    0,    0,   10;
    24,   30,   40,    0,    0,   26;
   160,  144,  180,  160,    0,    0, 76;
  1140, 1120, 1008,  840,  700,    0,  0, 232;
  8988, 9120, 8960, 5376, 4200, 2912,  0,   0, 764;
  ...

Crossrefs

Columns k=0-1 give: A038205, A221145.

Row sums give A000142.

Main diagonal gives A000085.

Cf. A007318.

Sequence in context: A089262 A325788 A240509 * A330619 A245693 A297866

Adjacent sequences: A344898 A344899 A344900 * A344902 A344903 A344904

Keyword

nonn,tabl

Author

Mikhail Kurkov, Jun 01 2021 [verification needed]

Status

approved