BinomialkoeffizientenBearbeiten
n\k |
−2 |
−1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7
|
8 |
9 |
10 |
11 |
12
|
---|
−4
|
0 |
0 |
1 |
−4 |
10 |
−20 |
35 |
−56 |
84 |
−120
|
165 |
−220 |
286 |
−364 |
455
|
---|
−3
|
0 |
0 |
1 |
−3 |
6 |
−10 |
15 |
−21 |
28 |
−36
|
45 |
−55 |
66 |
−78 |
91
|
---|
−2
|
0 |
0 |
1 |
−2 |
3 |
−4 |
5 |
−6 |
7 |
−8
|
9 |
−10 |
11 |
−12 |
13
|
---|
−1
|
0 |
0 |
1 |
−1 |
1 |
−1 |
1 |
−1 |
1 |
−1
|
1 |
−1 |
1 |
−1 |
1
|
---|
0
|
0
|
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
1
|
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
2
|
0 |
0 |
1 |
2 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
3
|
0 |
0 |
1 |
3 |
3 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
4
|
0 |
0 |
1 |
4 |
6 |
4 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
5
|
0 |
0 |
1 |
5 |
10 |
10 |
5 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
6
|
0 |
0 |
1 |
6 |
15 |
20 |
15 |
6 |
1 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
7
|
0 |
0 |
1 |
7 |
21 |
35 |
35 |
21 |
7 |
1 |
0 |
0 |
0 |
0 |
0
|
---|
8
|
0 |
0 |
1 |
8 |
28 |
56 |
70 |
56 |
28 |
8 |
1 |
0 |
0 |
0 |
0
|
---|
9
|
0 |
0 |
1 |
9 |
36 |
84 |
126 |
126 |
84 |
36 |
9 |
1 |
0 |
0 |
0
|
---|
10
|
0 |
0 |
1 |
10 |
45 |
120 |
210 |
252 |
210 |
120 |
45 |
10 |
1 |
0 |
0
|
---|
11
|
0 |
0 |
1 |
11 |
55 |
165 |
330 |
462 |
462 |
330 |
165 |
55 |
11 |
1 |
0
|
---|
12
|
0 |
0 |
1 |
12 |
66 |
220 |
495 |
792 |
924 |
792 |
495 |
220 |
66 |
12 |
1
|
---|
13
|
0 |
0 |
1 |
13 |
78 |
286 |
715 |
1287 |
1716 |
1716 |
1287 |
715 |
286 |
78 |
13
|
---|
14
|
0 |
0 |
1 |
14 |
91 |
364 |
1001 |
2002 |
3003 |
3432 |
3003 |
2002 |
1001 |
364 |
91
|
---|
Stirling-Zahlen erster ArtBearbeiten
n\k
|
−6 |
−5 |
−4 |
−3 |
−2 |
−1
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9
|
---|
−6
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−5
|
15 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−4
|
65 |
10 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−3
|
90 |
25 |
6 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−2
|
31 |
15 |
7 |
3 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−1
|
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
0
|
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
1
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
2
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
3
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
3 |
1 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
4
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
6 |
11 |
6 |
1 |
0 |
0 |
0 |
0 |
0
|
---|
5
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
24 |
50 |
35 |
10 |
1 |
0 |
0 |
0 |
0
|
---|
6
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
120 |
274 |
225 |
85 |
15 |
1 |
0 |
0 |
0
|
---|
7
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
720 |
1764 |
1624 |
735 |
175 |
21 |
1 |
0 |
0
|
---|
8
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
5040 |
13068 |
13132 |
6769 |
1960 |
322 |
28 |
1 |
0
|
---|
9
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
40320 |
109584 |
118124 |
67284 |
22449 |
4536 |
546 |
36 |
1
|
---|
Stirling-Zahlen zweiter ArtBearbeiten
n\k
|
−6 |
−5 |
−4 |
−3 |
−2 |
−1
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9
|
---|
−6
|
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−5
|
15 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−4
|
85 |
10 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−3
|
225 |
35 |
6 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−2
|
274 |
50 |
11 |
3 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
−1
|
120 |
24 |
6 |
2 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
0
|
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
1
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
2
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
3
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
3 |
1 |
0 |
0 |
0 |
0 |
0 |
0
|
---|
4
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
7 |
6 |
1 |
0 |
0 |
0 |
0 |
0
|
---|
5
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
15 |
25 |
10 |
1 |
0 |
0 |
0 |
0
|
---|
6
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
31 |
90 |
65 |
15 |
1 |
0 |
0 |
0
|
---|
7
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
63 |
301 |
350 |
140 |
21 |
1 |
0 |
0
|
---|
8
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
127 |
966 |
1701 |
1050 |
266 |
28 |
1 |
0
|
---|
9
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
255 |
3025 |
7770 |
6951 |
2646 |
462 |
36 |
1
|
---|
Berechnung am ComputerBearbeiten
Funktion |
Maxima |
GAP
|
---|
Binomialkoeffizient
|
binomial(n,k)
|
Binomial(n,k)
|
Stirling-Zahl erster Art
|
abs(stirling1(n,k))
|
Stirling1(n,k)
|
Stirling-Zahl zweiter Art
|
stirling2(n,k)
|
Stirling2(n,k)
|