A332784 The number of permutations of {n 1's, n 2's,...,n n's} with the property that b(1) >= b(2) >= ... >= b(n), where n k's are skipped by b(k) for k=1..n.

5, 18, 110, 508, 4968, 25824, 305376, 2375616, 28316832, 202354752, 4771240704, 33499830528, 612464852736, 9023719675392, 176001733301760, 1649576855476224, 56693983168309248, 551579829498390528, 20888523161929138176, 342595860998544285696

Offset

2,1

Links

Table of n, a(n) for n=2..21.

Formula

Conjecture: a(n) = A332783(n) + (n-1)!.

Example

In case of n = 2.
     |              | b(1),b(2)
-----+--------------+----------
   1 | [2, 2, 1, 1] | [0, 0]
   2 | [2, 1, 2, 1] | [1, 1]
   3 | [1, 2, 2, 1] | [2, 0]
   4 | [1, 2, 1, 2] | [1, 1]
   5 | [1, 1, 2, 2] | [0, 0]
In case of n = 3.
     |                             | b(1),b(2),b(3)
-----+-----------------------------+---------------
   1 | [3, 3, 3, 2, 2, 2, 1, 1, 1] | [0, 0, 0]
   2 | [3, 3, 3, 2, 1, 2, 1, 2, 1] | [1, 1, 0]
   3 | [3, 3, 3, 1, 2, 1, 2, 1, 2] | [1, 1, 0]
   4 | [3, 3, 3, 1, 1, 1, 2, 2, 2] | [0, 0, 0]
   5 | [3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]
   6 | [3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]
   7 | [1, 3, 3, 3, 1, 2, 2, 2, 1] | [3, 0, 0]
   8 | [2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]
   9 | [1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]
  10 | [2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]
  11 | [1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]
  12 | [2, 2, 2, 3, 3, 3, 1, 1, 1] | [0, 0, 0]
  13 | [1, 1, 1, 3, 3, 3, 2, 2, 2] | [0, 0, 0]
  14 | [1, 2, 2, 2, 1, 3, 3, 3, 1] | [3, 0, 0]
  15 | [2, 2, 2, 1, 1, 1, 3, 3, 3] | [0, 0, 0]
  16 | [2, 1, 2, 1, 2, 1, 3, 3, 3] | [1, 1, 0]
  17 | [1, 2, 1, 2, 1, 2, 3, 3, 3] | [1, 1, 0]
  18 | [1, 1, 1, 2, 2, 2, 3, 3, 3] | [0, 0, 0]

Crossrefs

Cf. A104442, A332762, A332783, A322178, A332748, A332752, A332773.

Sequence in context: A228614 A158455 A009442 * A302435 A332467 A036688

Adjacent sequences: A332781 A332782 A332783 * A332785 A332786 A332787

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2020

Extensions

a(9)-a(17) from Bert Dobbelaere, Mar 08 2020

a(18)-a(21) from Max Alekseyev, Sep 26 2023

Status

approved