Fungrim entry: 63f368

Table of

\left(n\right)^{\underline{k}}

for

0 \le n \le 10

and

0 \le k \le 10

$n$ \ $k$	0	1	2	3	4	5	6	7	8	9	10
0	1	0	0	0	0	0	0	0	0	0	0
1	1	1	0	0	0	0	0	0	0	0	0
2	1	2	2	0	0	0	0	0	0	0	0
3	1	3	6	6	0	0	0	0	0	0	0
4	1	4	12	24	24	0	0	0	0	0	0
5	1	5	20	60	120	120	0	0	0	0	0
6	1	6	30	120	360	720	720	0	0	0	0
7	1	7	42	210	840	2520	5040	5040	0	0	0
8	1	8	56	336	1680	6720	20160	40320	40320	0	0
9	1	9	72	504	3024	15120	60480	181440	362880	362880	0
10	1	10	90	720	5040	30240	151200	604800	1814400	3628800	3628800

Table data:

\left(n, k, y\right)

such that

\left(n\right)^{\underline{k}} = y

Definitions:

Fungrim symbol	Notation	Short description
`FallingFactorial`	$\left(z\right)^{\underline{k}}$	Falling factorial

Source code for this entry:

Entry(ID("63f368"),
    Description("Table of", FallingFactorial(n, k), "for", LessEqual(0, n, 10), "and", LessEqual(0, k, 10)),
    Table(TableRelation(Tuple(n, k, y), Equal(FallingFactorial(n, k), y)), TableHeadings(Description(n, "\", k), 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), TableColumnHeadings(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), List(Tuple(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 3, 6, 6, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 4, 12, 24, 24, 0, 0, 0, 0, 0, 0), Tuple(1, 5, 20, 60, 120, 120, 0, 0, 0, 0, 0), Tuple(1, 6, 30, 120, 360, 720, 720, 0, 0, 0, 0), Tuple(1, 7, 42, 210, 840, 2520, 5040, 5040, 0, 0, 0), Tuple(1, 8, 56, 336, 1680, 6720, 20160, 40320, 40320, 0, 0), Tuple(1, 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 362880, 0), Tuple(1, 10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800, 3628800))))

Fungrim entry: 63f368

Topics using this entry