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%I #24 Sep 26 2023 13:39:49
%S 5,18,110,508,4968,25824,305376,2375616,28316832,202354752,4771240704,
%T 33499830528,612464852736,9023719675392,176001733301760,
%U 1649576855476224,56693983168309248,551579829498390528,20888523161929138176,342595860998544285696
%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. A104442, A332762, A332783, A322178, A332748, A332752, A332773.
%K nonn
%O 2,1
%A _Seiichi Manyama_, Feb 23 2020
%E a(9)-a(17) from _Bert Dobbelaere_, Mar 08 2020
%E a(18)-a(21) from _Max Alekseyev_, Sep 26 2023