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A234574 T(n,k) is the number of size k ordered submultisets of the regular multiset {1_1,1_2,...,1_(n-1),1_n, ... ,i_1,i_2,...,i_(n-1),i_n, ... ,n_1,n_2,...,n_(n-1),n_n} (which contains n copies of i for 1 <= i <= n). 2
1, 1, 1, 1, 2, 4, 6, 6, 1, 3, 9, 27, 78, 210, 510, 1050, 1680, 1680, 1, 4, 16, 64, 256, 1020, 4020, 15540, 58380, 210840, 722400, 2310000, 6745200, 17417400, 37837800, 63063000, 63063000, 1, 5, 25, 125, 625, 3125, 15620, 77980, 388220, 1923180, 9454620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A181567 gives the case for unordered submultisets.

LINKS

Alois P. Heinz, Rows n = 0..26, flattened

Thomas Wieder, Maple program for A234574

EXAMPLE

For n=2 we have the regular multiset L = [1,1,2,2].

We get the following ordered submultisets from L:

For k=0 1 multiset: []

For k=1 2 multisets: [1], [2]

For k=2 4 multisets: [1,1], [1,2], [2,1], [2,2]

For k=3 6 multisets: [1,1,2], [1,2,1], [2,1,1], [1,2,2], [2,1,2], [2,2,1]

For k=4 6 multisets: [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1].

Triangle begins with:

  1;

  1, 1;

  1, 2, 4, 6, 6;

  1, 3, 9, 27, 78, 210, 510, 1050, 1680, 1680;

  1, 4, 16, 64, 256, 1020, 4020, 15540, 58380, 210840, 722400, 2310000, 6745200, 17417400, 37837800, 63063000, 63063000;

  ...

MAPLE

# first Maple program: see link above

# second Maple program:

b:= proc(n, k, i) option remember; `if`(k=0, 1,

     `if`(i<1, 0, add(b(n, k-j, i-1)/j!, j=0..n)))

    end:

T:= (n, k)-> b(n, k, n)*k!:

seq(seq(T(n, k), k=0..n^2), n=0..5); # Alois P. Heinz, Jul 04 2016

CROSSREFS

Cf. A181567.

Row sums give A274762.

Sequence in context: A055948 A071083 A141765 * A010587 A213473 A134920

Adjacent sequences:  A234571 A234572 A234573 * A234575 A234576 A234577

KEYWORD

nonn,tabf

AUTHOR

Thomas Wieder, Dec 29 2013

EXTENSIONS

More terms from Alois P. Heinz, Jul 04 2016

STATUS

approved

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Last modified August 2 20:38 EDT 2021. Contains 346428 sequences. (Running on oeis4.)