Simplify a combinatorial sum
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
149010
Finding Combinations to the provided Sum value
20443
Calculate sum of squares of first $n$ odd numbers
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
113331
Number of ways a natural number can be written as sum of smaller natural number
69194
Partitioning sum of squares
18064
Sum of reciprocals of numbers with certain terms omitted
99335
Sum of all triangle numbers
96585
Sums and permutation
482
Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form
39724
Combinatorial Identities
107964
Simple combinatorics problem.
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
104378
Minimizing weighted sum
68007
Sum or Product with Exclusions