Sum of binomials

Questions
1

Hi everyone.
I have a question related to what I’ve asked a while ago.

I would like to define a following sequence:
sum_(i=1)^k [ (k binomial i) * (i+1) ]
sum(j=1)^k (sum(i=1)^k [ (k binomial i)*(k binomial j) * (i+j+1) ]
sum(i=1)^k (sum(j=1)^k (sum_(t=1)^k [ (k binomial i)(k binomial j)(k binomial t) * (i+j+t) ]

etc.

Could you please help me with the correct algorithm? Many thanks!

D

2

(Refers to sequence of sums of binomial coefficients ?)

3

A helpful exercise would be to translate your pseudocode into Wolfram Language.

http://reference.wolfram.com/ and in the “Search Documentation” slot look for Sum and Binomial.

4

I found that inputting this complex expression gives quite a messy output. But you easily get a numerical result by setting k equal to some integer. Perhaps then make use of the results with k = 1, 2, 3 . . .

5

Thank you for the hint!

6

Thanks SM Blinder, in the end of the day I run simulations,so to run them I thought about having a formula as general as possible.
But yes, its quite a messy problem, my paper refers to extensions of binomial distributions, and its not the most elegant model:)

7

I think you’d get more help if the sums were translated to Wolfram Language as suggested by the Moderation Team.