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Link to the video here with timestamp In deriving the formula for regions of Moser's Circle Problem, it observed that the formula $$ F(x)=\binom{x}{4}+\binom{x}{2}+1 $$ achieves values that are equal ...

Resistance across opposite vertices of n-dimensional cube with each edge at one ohm resistance is $$R_n=\sum_{k=0}^{n-1}\frac1{(n-k){n\choose k}}=\frac1n\sum_{k=0}^{n-1}\frac1{{n-1\choose k}}.$$ The ...