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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

%I

%S 5,18,110,508,4968,25824,305376,2375616,28316832,202354752,4771240704,

%T 33499830528,612464852736,9023719675392,176001733301760,

%U 1649576855476224

%N 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.

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

%e In case of n = 2.

%e | | b(1),b(2)

%e -----+--------------+----------

%e 1 | [2, 2, 1, 1] | [0, 0]

%e 2 | [2, 1, 2, 1] | [1, 1]

%e 3 | [1, 2, 2, 1] | [2, 0]

%e 4 | [1, 2, 1, 2] | [1, 1]

%e 5 | [1, 1, 2, 2] | [0, 0]

%e In case of n = 3.

%e | | b(1),b(2),b(3)

%e -----+-----------------------------+---------------

%e 1 | [3, 3, 3, 2, 2, 2, 1, 1, 1] | [0, 0, 0]

%e 2 | [3, 3, 3, 2, 1, 2, 1, 2, 1] | [1, 1, 0]

%e 3 | [3, 3, 3, 1, 2, 1, 2, 1, 2] | [1, 1, 0]

%e 4 | [3, 3, 3, 1, 1, 1, 2, 2, 2] | [0, 0, 0]

%e 5 | [3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]

%e 6 | [3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]

%e 7 | [1, 3, 3, 3, 1, 2, 2, 2, 1] | [3, 0, 0]

%e 8 | [2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]

%e 9 | [1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]

%e 10 | [2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]

%e 11 | [1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]

%e 12 | [2, 2, 2, 3, 3, 3, 1, 1, 1] | [0, 0, 0]

%e 13 | [1, 1, 1, 3, 3, 3, 2, 2, 2] | [0, 0, 0]

%e 14 | [1, 2, 2, 2, 1, 3, 3, 3, 1] | [3, 0, 0]

%e 15 | [2, 2, 2, 1, 1, 1, 3, 3, 3] | [0, 0, 0]

%e 16 | [2, 1, 2, 1, 2, 1, 3, 3, 3] | [1, 1, 0]

%e 17 | [1, 2, 1, 2, 1, 2, 3, 3, 3] | [1, 1, 0]

%e 18 | [1, 1, 1, 2, 2, 2, 3, 3, 3] | [0, 0, 0]

%Y Cf. A332762, A332783.

%K nonn,more

%O 2,1

%A _Seiichi Manyama_, Feb 23 2020

%E a(9)-a(17) from _Bert Dobbelaere_, Mar 08 2020

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Last modified September 19 18:59 EDT 2020. Contains 337182 sequences. (Running on oeis4.)