Fungrim entry: fb5d88

Table of

{n \choose k}

for

0 \le n \le 15

and

0 \le k \le 15

$n$ \ $k$	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	1	2	1	0	0	0	0	0	0	0	0	0	0	0	0	0
3	1	3	3	1	0	0	0	0	0	0	0	0	0	0	0	0
4	1	4	6	4	1	0	0	0	0	0	0	0	0	0	0	0
5	1	5	10	10	5	1	0	0	0	0	0	0	0	0	0	0
6	1	6	15	20	15	6	1	0	0	0	0	0	0	0	0	0
7	1	7	21	35	35	21	7	1	0	0	0	0	0	0	0	0
8	1	8	28	56	70	56	28	8	1	0	0	0	0	0	0	0
9	1	9	36	84	126	126	84	36	9	1	0	0	0	0	0	0
10	1	10	45	120	210	252	210	120	45	10	1	0	0	0	0	0
11	1	11	55	165	330	462	462	330	165	55	11	1	0	0	0	0
12	1	12	66	220	495	792	924	792	495	220	66	12	1	0	0	0
13	1	13	78	286	715	1287	1716	1716	1287	715	286	78	13	1	0	0
14	1	14	91	364	1001	2002	3003	3432	3003	2002	1001	364	91	14	1	0
15	1	15	105	455	1365	3003	5005	6435	6435	5005	3003	1365	455	105	15	1

Table data:

\left(n, k, y\right)

such that

{n \choose k} = y

Definitions:

Fungrim symbol	Notation	Short description
`Binomial`	${n \choose k}$	Binomial coefficient

Source code for this entry:

Entry(ID("fb5d88"),
    Description("Table of", Binomial(n, k), "for", LessEqual(0, n, 15), "and", LessEqual(0, k, 15)),
    Table(TableRelation(Tuple(n, k, y), Equal(Binomial(n, k), y)), TableHeadings(Description(n, "\", k), 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), TableColumnHeadings(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), List(Tuple(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 7, 21, 35, 35, 21, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 0, 0), Tuple(1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 0, 0, 0, 0, 0), Tuple(1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 0, 0, 0, 0), Tuple(1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0), Tuple(1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1, 0, 0, 0), Tuple(1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0), Tuple(1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1, 0), Tuple(1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1))))

Fungrim entry: fb5d88

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