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A322093
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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.
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10
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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
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1,2
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LINKS
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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.
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FORMULA
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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.
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EXAMPLE
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Square array begins:
1, 2, 6, 24, 120, 720, ...
0, 2, 30, 864, 39480, 2631600, ...
0, 2, 174, 41304, 19606320, 16438575600, ...
0, 2, 1092, 2265024, 11804626080, 131402141197200, ...
0, 2, 7188, 134631576, 7946203275000, 1210527140790855600, ...
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CROSSREFS
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Columns k=3 gives A110706.
Rows n=1..10 give A000142, A114938, A193638, A321633, A322126, A321382, A322095, A322096, A322145, A322146.
Main diagonal gives A321634.
Cf. A322013.
Sequence in context: A095832 A248162 A143381 * A277681 A140876 A243997
Adjacent sequences: A322090 A322091 A322092 * A322094 A322095 A322096
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KEYWORD
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nonn,tabl
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AUTHOR
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Seiichi Manyama, Nov 26 2018
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STATUS
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approved
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