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A200473
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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).
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3
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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
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OFFSET
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1,7
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COMMENTS
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This sequence is A200472 with zeros removed.
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LINKS
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FORMULA
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T(n,k) = (n!/d_k!)/(n/d_k)!^d_k, n>=1, 1<=k<=tau(n), d_k = k-th divisor of n.
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EXAMPLE
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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;
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MAPLE
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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);
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MATHEMATICA
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row[n_] := (n!/#!)/(n/#)!^#& /@ Divisors[n];
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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