I have numerous conjectures raging around in my brain these days, but I am greatly lacking in the background needed to even attempt to prove them. I am interested in whatever is combinatorially known about sums of combinations, such as 0Cn + 1Cn + ... + nCn = 2**n, but of course everyone knows that one. Mine tend to involve situations modulo prime p where p is an odd prime. I am generally interested in where I might information about these things,l or be providedl with information about these things.
So please provided me with specific propositions, or books, or whatever. I particularly care about sums of jC2j, and interested in any combinatorial sums which get divided by j when we are at the j'th term, but I am generally interested in all of them.
I was once good at some aspects of mathematics, but combimatorics was truly never one of them.