Fungrim entry: 29741c

Table of

\left(n\right)_{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	2	6	24	120	720	5040	40320	362880	3628800
2	1	2	6	24	120	720	5040	40320	362880	3628800	39916800
3	1	3	12	60	360	2520	20160	181440	1814400	19958400	239500800
4	1	4	20	120	840	6720	60480	604800	6652800	79833600	1037836800
5	1	5	30	210	1680	15120	151200	1663200	19958400	259459200	3632428800
6	1	6	42	336	3024	30240	332640	3991680	51891840	726485760	10897286400
7	1	7	56	504	5040	55440	665280	8648640	121080960	1816214400	29059430400
8	1	8	72	720	7920	95040	1235520	17297280	259459200	4151347200	70572902400
9	1	9	90	990	11880	154440	2162160	32432400	518918400	8821612800	158789030400
10	1	10	110	1320	17160	240240	3603600	57657600	980179200	17643225600	335221286400

Table data:

\left(n, k, y\right)

such that

\left(n\right)_{k} = y

Definitions:

Fungrim symbol	Notation	Short description
`RisingFactorial`	$\left(z\right)_{k}$	Rising factorial

Source code for this entry:

Entry(ID("29741c"),
    Description("Table of", RisingFactorial(n, k), "for", LessEqual(0, n, 10), "and", LessEqual(0, k, 10)),
    Table(TableRelation(Tuple(n, k, y), Equal(RisingFactorial(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, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800), Tuple(1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800), Tuple(1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800), Tuple(1, 4, 20, 120, 840, 6720, 60480, 604800, 6652800, 79833600, 1037836800), Tuple(1, 5, 30, 210, 1680, 15120, 151200, 1663200, 19958400, 259459200, 3632428800), Tuple(1, 6, 42, 336, 3024, 30240, 332640, 3991680, 51891840, 726485760, 10897286400), Tuple(1, 7, 56, 504, 5040, 55440, 665280, 8648640, 121080960, 1816214400, 29059430400), Tuple(1, 8, 72, 720, 7920, 95040, 1235520, 17297280, 259459200, 4151347200, 70572902400), Tuple(1, 9, 90, 990, 11880, 154440, 2162160, 32432400, 518918400, 8821612800, 158789030400), Tuple(1, 10, 110, 1320, 17160, 240240, 3603600, 57657600, 980179200, 17643225600, 335221286400))))

Fungrim entry: 29741c

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