A124774 Multinomial coefficients for compositions in standard order.

1, 1, 1, 2, 1, 3, 3, 6, 1, 4, 6, 12, 4, 12, 12, 24, 1, 5, 10, 20, 10, 30, 30, 60, 5, 20, 30, 60, 20, 60, 60, 120, 1, 6, 15, 30, 20, 60, 60, 120, 15, 60, 90, 180, 60, 180, 180, 360, 6, 30, 60, 120, 60, 180, 180, 360, 30, 120, 180, 360, 120, 360, 360, 720, 1, 7, 21, 42, 35, 105

Offset

0,4

Comments

The standard order of compositions is given by A066099.

Number of ways to distribute labeled objects into boxes, with the number of objects in each box being specified by the composition.

Links

Alois P. Heinz, Rows n = 0..14, flattened

Formula

For composition b(1),...,b(k), a(n) = (Sum_{i=1}^k b(i))! / (Product_{i=1}^k b(i)!).

Example

Composition number 11 is 2,1,1; there are 6 choices for the pair of objects in the first box, then 2 choices for the object in the next box, so a(11) = 6*2 = 12.
The table starts:
1
1
1 2
1 3 3 6

Crossrefs

Cf. A066099, A124773, A011782 (row lengths), A000670 (row sums), A036039.

Sequence in context: A132883 A132888 A213934 * A056610 A341450 A343381

Adjacent sequences: A124771 A124772 A124773 * A124775 A124776 A124777

Keyword

easy,nonn,tabf

Author

Franklin T. Adams-Watters, Nov 06 2006

Status

approved