The On-Line Encyclopedia of Integer Sequences (OEIS)

A322093 revision #31

A322093

Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the number of permutations of n copies of 1..k with no element equal to another within a distance of 1.

1, 2, 0, 6, 2, 0, 24, 30, 2, 0, 120, 864, 174, 2, 0, 720, 39480, 41304, 1092, 2, 0, 5040, 2631600, 19606320, 2265024, 7188, 2, 0, 40320, 241133760, 16438575600, 11804626080, 134631576, 48852, 2, 0, 362880, 29083420800, 22278418248240, 131402141197200, 7946203275000, 8437796016, 339720, 2, 0

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OFFSET

1,2

LINKS

Seiichi Manyama, Antidiagonals n = 1..52, flattened

Mathematics.StackExchange, Find the number of k 1's, k 2's, ... , k n's - total kn cards, Apr 08 2012.

FORMULA

A(n,k) = k! * A322013(n,k).

Let q_n(x) = Sum_{i=1..n} (-1)^(n-i) * binomial(n-1, n-i) * x^i/i!.

A(n,k) = Integral_{0..infinity} (q_n(x))^k * exp(-x) dx.

EXAMPLE

Square array begins: