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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. 2
5, 18, 110, 508, 4968, 25824, 305376, 2375616, 28316832, 202354752, 4771240704, 33499830528, 612464852736, 9023719675392, 176001733301760, 1649576855476224 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Table of n, a(n) for n=2..17.

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. A332762, A332783.

Sequence in context: A228614 A158455 A009442 * A302435 A332467 A036688

Adjacent sequences:  A332781 A332782 A332783 * A332785 A332786 A332787

KEYWORD

nonn,more

AUTHOR

Seiichi Manyama, Feb 23 2020

EXTENSIONS

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

STATUS

approved

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Last modified August 11 05:42 EDT 2020. Contains 336422 sequences. (Running on oeis4.)