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 A275069 Number A(n,k) of set partitions of [n] such that i-j is a multiple of k for all i,j belonging to the same block; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 15, 1, 1, 1, 1, 1, 4, 52, 1, 1, 1, 1, 1, 2, 10, 203, 1, 1, 1, 1, 1, 1, 4, 25, 877, 1, 1, 1, 1, 1, 1, 2, 8, 75, 4140, 1, 1, 1, 1, 1, 1, 1, 4, 20, 225, 21147, 1, 1, 1, 1, 1, 1, 1, 2, 8, 50, 780, 115975, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened Wikipedia, Partition of a set FORMULA A(n,k) = Product_{i=0..k-1} A000110(floor((n+i)/k)). EXAMPLE A(5,0) = 1: 1|2|3|4|5. A(5,1) = 52 = A000110(5). A(5,2) = 10: 135|24, 13|24|5, 135|2|4, 13|2|4|5, 15|24|3, 1|24|35, 1|24|3|5, 15|2|3|4, 1|2|35|4, 1|2|3|4|5. A(5,3) = 4: 14|25|3, 14|2|3|5, 1|25|3|4, 1|2|3|4|5. A(5,4) = 2: 15|2|3|4, 1|2|3|4|5. 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,      5,    2,   1,   1,  1,  1, 1, 1, 1, 1, ...   1,     15,    4,   2,   1,  1,  1, 1, 1, 1, 1, ...   1,     52,   10,   4,   2,  1,  1, 1, 1, 1, 1, ...   1,    203,   25,   8,   4,  2,  1, 1, 1, 1, 1, ...   1,    877,   75,  20,   8,  4,  2, 1, 1, 1, 1, ...   1,   4140,  225,  50,  16,  8,  4, 2, 1, 1, 1, ...   1,  21147,  780, 125,  40, 16,  8, 4, 2, 1, 1, ...   1, 115975, 2704, 375, 100, 32, 16, 8, 4, 2, 1, ... MAPLE with(combinat): A:= (n, k)-> mul(bell(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[BellB[Floor[(n+i)/k]], {i, 0, k-1}]; Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 17 2017, translated from Maple *) CROSSREFS Columns k=0-10 give: A000012, A000110, A124419, A275070, A275071, A275072, A275073, A275074, A275075, A275076, A275077. A(k*n,n) for k=1-4 gives: A000012, A000079, A000351, A001024. Sequence in context: A212363 A212382 A274835 * A181937 A233836 A214719 Adjacent sequences:  A275066 A275067 A275068 * A275070 A275071 A275072 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 15 2016 STATUS approved

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Last modified June 16 13:05 EDT 2021. Contains 345057 sequences. (Running on oeis4.)