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A249620 Triangle read by rows: T(m,n) = number of partitions of the multiset with m elements and signature corresponding to n-th integer partition (A194602). 6
1, 1, 2, 2, 5, 4, 3, 15, 11, 7, 9, 5, 52, 36, 21, 26, 12, 16, 7, 203, 135, 74, 92, 38, 52, 19, 66, 29, 31, 11, 877, 566, 296, 371, 141, 198, 64, 249, 98, 109, 30, 137, 47, 57, 15, 4140, 2610, 1315, 1663, 592, 850, 250, 1075, 392, 444, 105, 560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This triangle shows the same numbers in each row as A129306 and A096443, but in this arrangement the multisets in column n correspond to the n-th integer partition in the infinite order defined by A194602.

Triangle begins:

  n     0    1   2   3   4   5   6   7   8   9  10

m

0       1

1       1

2       2    2

3       5    4   3

4      15   11   7   9   5

5      52   36  21  26  12  16   7

6     203  135  74  92  38  52  19  66  29  31  11

Row lengths: A000041 (partition numbers), Row sums: A035310

Columns: 0: A000110 (Bell), 1: A035098 (near-Bell), 2: A169587, 4: A169588

Last in row: end-1: A091437, end: A000041 (partition numbers)

The rightmost columns form a reflected version of the triangle A126442:

  n      0     1     2     4    6   10  14  21      (A000041(1,2,3...)-1)

m

1        1

2        2     2

3        5     4     3

4       15    11     7     5

5       52    36    21    12    7

6      203   135    74    38   19   11

7      877   566   296   141   64   30  15

8     4140  2610  1315   592  250  105  45  22

A249619 shows the number of permutations of the same multisets.

LINKS

Tilman Piesk, Triangle rows m=0..8, flattened.

Tilman Piesk, Partitions of multisets (Wikiversity)

Tilman Piesk, The T(5,2)=21 partitions of {1,1,1,2,3}

Tilman Piesk, PHP code used to calculate the examples

EXAMPLE

See "The T(5,2)=21 partitions of {1,1,1,2,3}" link. Similar links for m=1..8 are in "Partitions of multisets" (Wikiversity).

CROSSREFS

Cf. A129306, A096443, A035310, A194602, A249619, A000041, A126442

Sequence in context: A209761 A228526 A209745 * A025498 A193693 A128971

Adjacent sequences:  A249617 A249618 A249619 * A249621 A249622 A249623

KEYWORD

nonn,tabf

AUTHOR

Tilman Piesk, Nov 04 2014

STATUS

approved

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Last modified May 23 07:00 EDT 2019. Contains 323508 sequences. (Running on oeis4.)