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 A200473 Irregular triangle read by rows: T(n,k) = number of ways to assign n people to d_k unlabeled groups of equal size (where d_k is the k-th divisor of n). 3
 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 10, 15, 1, 1, 1, 1, 35, 105, 1, 1, 280, 1, 1, 126, 945, 1, 1, 1, 1, 462, 5775, 15400, 10395, 1, 1, 1, 1, 1716, 135135, 1, 1, 126126, 1401400, 1, 1, 6435, 2627625, 2027025, 1, 1, 1, 1, 24310, 2858856, 190590400, 34459425, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS This sequence is A200472 with zeros removed. LINKS Alois P. Heinz, Rows n = 1..250, flattened Dennis P. Walsh, Note on assigning n people to k unlabeled groups of equal size FORMULA T(n,k) = (n!/d_k!)/(n/d_k)!^d_k, n>=1, 1<=k<=tau(n), d_k = k-th divisor of n. Sum_{k=1..tau(k)} T(n,k) = A038041(n). - Alois P. Heinz, Jul 22 2016 EXAMPLE T(n,k) begins: 1; 1,      1; 1,      1; 1,      3,       1; 1,      1; 1,     10,      15,       1; 1,      1; 1,     35,     105,       1; 1,    280,       1; 1,    126,     945,       1; 1,      1; 1,    462,    5775,   15400, 10395,   1; 1,      1; 1,   1716,  135135,       1; 1, 126126, 1401400,       1; 1,   6435, 2627625, 2027025,     1; MAPLE with(numtheory): S:= n-> sort([divisors(n)[]]): T:= (n, k)-> n!/(S(n)[k])!/((n/(S(n)[k]))!)^(S(n)[k]): seq(seq(T(n, k), k=1..tau(n)), n=1..10); MATHEMATICA row[n_] := (n!/#!)/(n/#)!^#& /@ Divisors[n]; Table[row[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Mar 24 2017 *) CROSSREFS Cf. A200472, A000005 (row lengths). Cf. A038041 (row sums). Sequence in context: A054724 A061494 A141901 * A180172 A327372 A328323 Adjacent sequences:  A200470 A200471 A200472 * A200474 A200475 A200476 KEYWORD nonn,tabf AUTHOR Dennis P. Walsh, Nov 18 2011 STATUS approved

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Last modified February 21 18:03 EST 2020. Contains 332103 sequences. (Running on oeis4.)