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A124774
Multinomial coefficients for compositions in standard order.
3
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
Thomas Garrity and Jacob Lehmann Duke, Ergodicity and Algebraticity of the Fast and Slow Triangle Maps, arXiv:2409.05822 [math.DS], 2024. See p. 22.
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
KEYWORD
easy,nonn,tabf
AUTHOR
STATUS
approved