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 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. 10
 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 (list; table; graph; refs; listen; history; text; internal format)
 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:    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, ... CROSSREFS 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 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Nov 26 2018 STATUS approved

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)