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 A275062 Number A(n,k) of permutations p of [n] such that p(i)-i is a multiple of k for all i in [n]; square array A(n,k), n>=0, k>=0, read by antidiagonals. 15
 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 6, 1, 1, 1, 1, 2, 24, 1, 1, 1, 1, 1, 4, 120, 1, 1, 1, 1, 1, 2, 12, 720, 1, 1, 1, 1, 1, 1, 4, 36, 5040, 1, 1, 1, 1, 1, 1, 2, 8, 144, 40320, 1, 1, 1, 1, 1, 1, 1, 4, 24, 576, 362880, 1, 1, 1, 1, 1, 1, 1, 2, 8, 72, 2880, 3628800, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened FORMULA A(n,k) = Product_{i=0..k-1} floor((n+i)/k)!. A(k*n,k) = (n!)^k = A225816(k,n). For k > 0, A(n, k) ~ (2*Pi*n)^((k - 1)/2) * n! / k^(n + k/2). - Vaclav Kotesovec, Oct 02 2018 EXAMPLE A(5,0) = A(5,5) = 1: 12345. A(5,1) = 5! = 120: all permutations of {1,2,3,4,5}. A(5,2) = 12: 12345, 12543, 14325, 14523, 32145, 32541, 34125, 34521, 52143, 52341, 54123, 54321. A(5,3) = 4: 12345, 15342, 42315, 45312. A(5,4) = 2: 12345, 52341. A(7,4) = 8: 1234567, 1274563, 1634527, 1674523, 5234167, 5274163, 5634127, 5674123. Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 24, 4, 2, 1, 1, 1, 1, 1, 1, 1, ... 1, 120, 12, 4, 2, 1, 1, 1, 1, 1, 1, ... 1, 720, 36, 8, 4, 2, 1, 1, 1, 1, 1, ... 1, 5040, 144, 24, 8, 4, 2, 1, 1, 1, 1, ... 1, 40320, 576, 72, 16, 8, 4, 2, 1, 1, 1, ... 1, 362880, 2880, 216, 48, 16, 8, 4, 2, 1, 1, ... 1, 3628800, 14400, 864, 144, 32, 16, 8, 4, 2, 1, ... MAPLE A:= (n, k)-> mul(floor((n+i)/k)!, i=0..k-1): seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA A[n_, k_] := Product[Floor[(n+i)/k]!, {i, 0, k-1}]; Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 26 2019, from Maple *) CROSSREFS Columns k=0-10 give: A000012, A000142, A010551, A264557, A264635, A264656, A264701, A264791, A275063, A275064, A275065. A(k*n,n) for k=1..4 give: A000012, A000079, A000400, A009968. Cf. A225816. Sequence in context: A146314 A202480 A124341 * A247005 A174215 A364457 Adjacent sequences: A275059 A275060 A275061 * A275063 A275064 A275065 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 15 2016 STATUS approved

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Last modified October 1 14:33 EDT 2023. Contains 365826 sequences. (Running on oeis4.)