How Do Stirling Numbers of the First Kind Relate to Combinatorial Formulas?

  • Thread starter Thread starter pleasehelp328
  • Start date Start date
  • Tags Tags
    Proof
pleasehelp328
Messages
3
Reaction score
0
Say we have sterling numbers of the first kind where we're given s(n, n-2) = 2(nC3) + 3(nC4)
for n greater than or equal to 4.

I know the left hand side we have n people, and we wish to seat them at n-2 circular tables, but I need help with the right hand side! I would greatly appreciate any help at ALL!
 
Physics news on Phys.org
Any math experts willing to help?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Sterling numbers of the First kind Combinatorial Proof
Replies
1
Views
2K
Deduce orthogonality relations for sine and cosine w/ Euler's Formula
Replies
1
Views
1K
Proof of an inequality with natural numbers
Replies
3
Views
2K
How Does Sum of Consecutive Numbers Relate to Cubes of Integers?
Replies
2
Views
2K
Combinatorial Proofs of Binomial Identities
Replies
9
Views
8K
Stirling's Formula: How does n relate to n^n.
Replies
3
Views
1K
Difficult number theory problem proofs
Replies
3
Views
2K
A discrete-time queue Markov Chain problem
Replies
12
Views
2K
Technique for proving Inclusion-Exclusion principle combinatorically
Replies
5
Views
3K
How to disprove (m^2)+m+1=(n^2)?
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top