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 A275422 Number A(n,k) of set partitions of [n] such that k is a multiple of each block size; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 1, 15, 1, 1, 1, 4, 1, 52, 1, 1, 2, 2, 10, 1, 203, 1, 1, 1, 4, 5, 26, 1, 877, 1, 1, 2, 1, 11, 11, 76, 1, 4140, 1, 1, 1, 5, 1, 31, 31, 232, 1, 21147, 1, 1, 2, 1, 14, 2, 106, 106, 764, 1, 115975, 1, 1, 1, 4, 1, 46, 7, 372, 337, 2620, 1, 678570 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Antidiagonals n = 0..200, flattened Wikipedia, Partition of a set FORMULA E.g.f. for column k>0: exp(Sum_{d|k} x^d/d!), for k=0: exp(exp(x)-1). EXAMPLE A(5,3) = 11: 123|4|5, 124|3|5, 125|3|4, 134|2|5, 135|2|4, 1|234|5, 1|235|4, 145|2|3, 1|245|3, 1|2|345, 1|2|3|4|5. A(4,4) = 11: 1234, 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|24|3, 1|2|34, 1|2|3|4. A(6,5) = 7: 12345|6, 12346|5, 12356|4, 12456|3, 13456|2, 1|23456, 1|2|3|4|5|6. Square array A(n,k) begins: :    1, 1,   1,   1,    1,  1,    1, 1,    1, ... :    1, 1,   1,   1,    1,  1,    1, 1,    1, ... :    2, 1,   2,   1,    2,  1,    2, 1,    2, ... :    5, 1,   4,   2,    4,  1,    5, 1,    4, ... :   15, 1,  10,   5,   11,  1,   14, 1,   11, ... :   52, 1,  26,  11,   31,  2,   46, 1,   31, ... :  203, 1,  76,  31,  106,  7,  167, 1,  106, ... :  877, 1, 232, 106,  372, 22,  659, 2,  372, ... : 4140, 1, 764, 337, 1499, 57, 2836, 9, 1500, ... MAPLE A:= proc(n, k) option remember; `if`(n=0, 1, add(       `if`(j>n, 0, A(n-j, k)*binomial(n-1, j-1)), j=       `if`(k=0, 1..n, numtheory[divisors](k))))     end: seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA A[n_, k_] := A[n, k] = If[n==0, 1, Sum[If[j>n, 0, A[n-j, k]*Binomial[n-1, j - 1]], {j, If[k==0, Range[n], Divisors[k]]}]]; Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *) CROSSREFS Columns k=0-10 give: A000110, A000012, A000085, A190865, A190452, A275423, A275424, A275425, A275426, A275427, A275428. Main diagonal gives A275429. Sequence in context: A213945 A290771 A014651 * A169951 A174453 A082063 Adjacent sequences:  A275419 A275420 A275421 * A275423 A275424 A275425 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 27 2016 STATUS approved

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)