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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-Fran├žois 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.)