A249619 Triangle T(m,n) = number of permutations of a multiset with m elements and signature corresponding to n-th integer partition (A194602).

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

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.

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

Example

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

Crossrefs

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

Sequence in context: A138533 A173333 A221915 * A345462 A222159 A221623

Adjacent sequences: A249616 A249617 A249618 * A249620 A249621 A249622

Keyword

nonn,tabf

Author

Tilman Piesk, Nov 04 2014

Status

approved