A362192 - OEIS

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.

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

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OFFSET

1,3

COMMENTS

Provides the same counts as A361296, but up to a choice for the first payphone.

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..100

Max A. Alekseyev, Enumeration of Payphone Permutations, arXiv:2304.04324 [math.CO], 2023.

FORMULA

a(n) = A361296(n) / n.

CROSSREFS

Cf. A095236, A095239, A095240, A095912, A358056, A361294, A361295, A361296.