login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A249619 Triangle T(m,n) = number of permutations of a multiset with m elements and signature corresponding to n-th integer partition (A194602). 2
1, 1, 2, 1, 6, 3, 1, 24, 12, 4, 6, 1, 120, 60, 20, 30, 5, 10, 1, 720, 360, 120, 180, 30, 60, 6, 90, 15, 20, 1, 5040, 2520, 840, 1260, 210, 420, 42, 630, 105, 140, 7, 210, 21, 35, 1, 40320, 20160, 6720, 10080, 1680, 3360, 336, 5040, 840, 1120, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This triangle shows the same numbers in each row as A036038 and A078760 (the multinomial coefficients), 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    1

3       6    3    1

4      24   12    4    6   1

5     120   60   20   30   5  10  1

6     720  360  120  180  30  60  6  90  15  20  1

Row lengths: A000041 (partition numbers), Row sums: A005651

Columns: 0: A000142 (factorials), 1: A001710, 2: A001715, 3: A133799, 4: A001720, 6: A001725, 10: A001730, 14: A049388

Last in row: end-2: A037955 after 1 term mismatch, end-1: A001405, end: A000012

The rightmost columns form the triangle A173333:

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

m

1         1

2         2      1

3         6      3     1

4        24     12     4     1

5       120     60    20     5    1

6       720    360   120    30    6   1

7      5040   2520   840   210   42   7   1

8     40320  20160  6720  1680  336  56   8   1

A249620 shows the number of partitions of the same multisets. A187783 shows the number of permutations of special multisets.

LINKS

Tilman Piesk, Triangle rows m=0..25, flattened

Tilman Piesk, Illustration of the multisets for m=0..6

CROSSREFS

Cf. A036038, A078760, A005651, A005651, A249620, A000041, A173333.

Sequence in context: A138533 A173333 A221915 * A222159 A221623 A096334

Adjacent sequences:  A249616 A249617 A249618 * A249620 A249621 A249622

KEYWORD

nonn,tabf

AUTHOR

Tilman Piesk, Nov 04 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)