Fungrim entry: cecede

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	1	3	1	0	0	0	0	0	0	0
4	0	1	7	6	1	0	0	0	0	0	0
5	0	1	15	25	10	1	0	0	0	0	0
6	0	1	31	90	65	15	1	0	0	0	0
7	0	1	63	301	350	140	21	1	0	0	0
8	0	1	127	966	1701	1050	266	28	1	0	0
9	0	1	255	3025	7770	6951	2646	462	36	1	0
10	0	1	511	9330	34105	42525	22827	5880	750	45	1

Table data:

\left(n, k, y\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`StirlingS2`	$\left\{{n \atop k}\right\}$	Stirling number of the second kind

Source code for this entry:

Entry(ID("cecede"),
    Description("Table of", StirlingS2(n, k), "for", LessEqual(0, n, 10), "and", LessEqual(0, k, 10)),
    Table(TableRelation(Tuple(n, k, y), Equal(StirlingS2(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, 1, 3, 1, 0, 0, 0, 0, 0, 0, 0), Tuple(0, 1, 7, 6, 1, 0, 0, 0, 0, 0, 0), Tuple(0, 1, 15, 25, 10, 1, 0, 0, 0, 0, 0), Tuple(0, 1, 31, 90, 65, 15, 1, 0, 0, 0, 0), Tuple(0, 1, 63, 301, 350, 140, 21, 1, 0, 0, 0), Tuple(0, 1, 127, 966, 1701, 1050, 266, 28, 1, 0, 0), Tuple(0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1, 0), Tuple(0, 1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1))))

Topics using this entry

Stirling numbers