Matematické Fórum

stuart clark · 28. 01. 2019 06:48

Evaluation of $\displaystyle \mathop{\sum\sum\sum\sum}_{1\leq i \leq j<k\leq w \leq n}1$

laszky · 28. 01. 2019 23:15 — Editoval laszky (29. 01. 2019 02:25)

stuart clark

Thanks ↑ laszky:.

I have one more binomial problem

Evaluation of $\frac{\sum^{r}_{k=0}\binom{n}{k}\binom{n-2k}{r-k}}{\sum^{n}_{k=r}\binom{n}{k}\binom{2k}{2r}(\frac{3}{4})^{n-k}(\frac{1}{2})^{2k-2r}}$ For $(n\geq 2r)$

please see that problem

stuart clark · 30. 04. 2019 16:43

@ Laszky I am Trying that problem using

Coefficient of $x^{2r}$ in $(1+x+x^2)^{n}=\bigg[1+x(1+x)\bigg]^n=\bigg[\bigg(x+\frac{1}{2}\bigg)^2+\frac{3}{4}\bigg]^n$

But could not find end result, please show me how to get it

Thank You

Marian · 02. 05. 2019 16:24 — Editoval Marian (02. 05. 2019 16:25)

↑ stuart clark:

Note to your first problem:

There is a free paper from Butler (2010), see the PDF version here, that discuss your sum. Also, certain generalizations are mentioned that could be of some importance to you.

stuart clark · 04. 05. 2019 09:48

Thanks ↑ Marian:

Matematické Fórum

#1 28. 01. 2019 06:48

Binomial coefficients

#2 28. 01. 2019 23:15 — Editoval laszky (29. 01. 2019 02:25)

Re: Binomial coefficients

#3 29. 01. 2019 18:48 — Editoval stuart clark (29. 01. 2019 18:51)

Re: Binomial coefficients

#4 30. 04. 2019 16:43

Re: Binomial coefficients

#5 02. 05. 2019 16:24 — Editoval Marian (02. 05. 2019 16:25)

Re: Binomial coefficients

#6 04. 05. 2019 09:48

Re: Binomial coefficients

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