A259553 Number of distinct (n!)-tuples, with integer entries between 0 and n, inclusive, where entries measure the length of the longest prefix of each of the n! permutations of 123...n that is a subsequence of some string over the alphabet {1,2,3,...n}.
2, 6, 53, 12034
Offset: 1
Examples
For n = 2, where the permutations are 12 and 21, the six possible 2-tuples are (0,0) (corresponding to the empty string); (1,0) (corresponding to 1); (0,1) (corresponding to 2); (2,1) (corresponding to 12); (1,2) (corresponding to 21); (2,2) (corresponding to 121).
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