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Specific values of factorials and binomial coefficients

Table of contents: Tables - Special cases

Related topics: Factorials and binomial coefficients

Tables

3009a7
Table of n!n ! for 0n300 \le n \le 30
fb5d88
Table of (nk){n \choose k} for 0n150 \le n \le 15 and 0k150 \le k \le 15
29741c
Table of (n)k\left(n\right)_{k} for 0n100 \le n \le 10 and 0k100 \le k \le 10
63f368
Table of (n)k\left(n\right)^{\underline{k}} for 0n100 \le n \le 10 and 0k100 \le k \le 10

Special cases

d8c274
0!=10 ! = 1
988310
(n0)=1{n \choose 0} = 1
8c21f5
(nn)=1{n \choose n} = 1
471485
(nn+m)=0{n \choose n + m} = 0
5b85bf
(z1)=z{z \choose 1} = z
1df686
(z2)=z(z1)2{z \choose 2} = \frac{z \left(z - 1\right)}{2}
e78084
(z)0=1\left(z\right)_{0} = 1
973b2c
(z)1=z\left(z\right)_{1} = z
0feb19
(1)k=k!\left(1\right)_{k} = k !
5b414d
(z)0=1\left(z\right)^{\underline{0}} = 1
a7b330
(z)1=z\left(z\right)^{\underline{1}} = z
355c22
(k)k=k!\left(k\right)^{\underline{k}} = k !
0d92f6
(2nn)=(2n)!(n!)2{2 n \choose n} = \frac{\left(2 n\right)!}{{\left(n !\right)}^{2}}

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-21 11:44:15.926409 UTC