Fungrim entry: f88455

Table of

\left[{n \atop k}\right]

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	0	1	0	0	0	0	0	0	0	0	0
2	0	1	1	0	0	0	0	0	0	0	0
3	0	2	3	1	0	0	0	0	0	0	0
4	0	6	11	6	1	0	0	0	0	0	0
5	0	24	50	35	10	1	0	0	0	0	0
6	0	120	274	225	85	15	1	0	0	0	0
7	0	720	1764	1624	735	175	21	1	0	0	0
8	0	5040	13068	13132	6769	1960	322	28	1	0	0
9	0	40320	109584	118124	67284	22449	4536	546	36	1	0
10	0	362880	1026576	1172700	723680	269325	63273	9450	870	45	1

Table data:

\left(n, k, y\right)

such that

\left[{n \atop k}\right] = y

Definitions:

Fungrim symbol	Notation	Short description
`StirlingCycle`	$\left[{n \atop k}\right]$	Unsigned Stirling number of the first kind

Source code for this entry:

Entry(ID("f88455"),
    Description("Table of", StirlingCycle(n, k), "for", LessEqual(0, n, 10), "and", LessEqual(0, k, 10)),
    Table(TableRelation(Tuple(n, k, y), Equal(StirlingCycle(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(0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(0, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0), Tuple(0, 6, 11, 6, 1, 0, 0, 0, 0, 0, 0), Tuple(0, 24, 50, 35, 10, 1, 0, 0, 0, 0, 0), Tuple(0, 120, 274, 225, 85, 15, 1, 0, 0, 0, 0), Tuple(0, 720, 1764, 1624, 735, 175, 21, 1, 0, 0, 0), Tuple(0, 5040, 13068, 13132, 6769, 1960, 322, 28, 1, 0, 0), Tuple(0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1, 0), Tuple(0, 362880, 1026576, 1172700, 723680, 269325, 63273, 9450, 870, 45, 1))))

Topics using this entry

Stirling numbers