I need hints on a direction to prove that
$$\displaystyle\prod_{k=1}^{n} {{k+1\choose2}\choose k} ={{n+1\choose2}\choose1,2,3.....,n}$$
Any ideas?
2026-03-25 17:44:57.1774460697
Multinomial identity - guidance needed
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Hint: every multinomial coefficient is a product of binomial coefficients similar to this one. For example, $$\binom{3n-3}{n,n-1,n-2}=\binom{3n-3}{n} \binom{2n-3}{n-1} \binom{n-2}{n-2}$$