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A362192
A variant of payphone permutations: given a circular booth with n payphones, one of which is already occupied, a(n) is the number ways for n-1 people to choose the payphones in order, where each person chooses an unoccupied payphone such that the closest occupied payphone is as distant as possible.
6
1, 1, 2, 2, 12, 24, 48, 48, 960, 5760, 20160, 80640, 322560, 645120, 967680, 1935360, 139345920, 2786918400, 30656102400, 367873228800, 2391175987200, 11158821273600, 62768369664000, 1004293914624000, 8034351316992000, 32137405267968000, 96412215803904000, 385648863215616000, 964122158039040000, 1928244316078080000
OFFSET
1,3
COMMENTS
Provides the same counts as A361296, but up to a choice for the first payphone.
LINKS
Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.
FORMULA
a(n) = A361296(n) / n.
KEYWORD
nonn
AUTHOR
Max Alekseyev, Apr 10 2023
STATUS
approved