Number after binomial coefficient

Question

What does the number 2 mean in this picture? enter image description here link

Thanks. Sorry I'm not a math expert.

I need this to make a program in C to generate a trinomial triangle for a guy who asked it on StackOverflow (it is his homework). Gotta earn that reputation. You know how it is!

I find this a horrible notataion. For me $\binom nk_2$ is the Gaussian binomial coefficient $\binom nk_q$ evaluated at $q=2$, which is quite something different. — Marc van Leeuwen, Sep 03 '14 at 11:43

RE60K · Accepted Answer · 2014-09-02T11:10:37.870

2

Scroll down the page you mentioned to see:

enter image description here

Actually it is the sum of of $x^k$ in $(1+x+1/x)^n$. For e.g.: In $$(1+x+x)^3=x^3+\frac1{x^3}+3 x^2+\frac3{x^2}+6 x+\frac6x+7$$ $$\binom 33_2=1,\binom3{-3}_2=1,\binom32_2=3,\binom3{-2}_2=3,\binom31_2=6,\binom3{-1}_2=6,\binom30_2=7 $$ Let's calulate $\binom42_2$: $$\binom42_2=\underbrace{\frac{4!}{4!1!(4-4-1)!}}_{\mu=4,\;\nu=1}+\underbrace{\frac{4!}{2!2!(4-2-2)!}}_{\mu=2,\;\nu=2}+\underbrace{\frac{4!}{0!3!(4-0-3)!}}_{\mu=0,\;\nu=3}$$

edited Sep 02 '14 at 11:10

answered Sep 02 '14 at 09:27

RE60K

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@GerryMyerson does the edit satisfy you? – RE60K Sep 02 '14 at 11:11

Number after binomial coefficient

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