#1535 · Algebra · Sequences & series

Sum Identity with Triangular Numbers

If $s_{n}$ denote the sum of the first $n$ natural numbers, prove that $2 (s_{1} s_{2 n} + s_{2} s_{2 n - 1} + \dots + s_{n} s_{n + 1}) = \frac{( 2 n + 4 )!}{5 ! ( 2 n - 1 )!}$ .

~25 minProof · checked by AIBinomial TheoremCoefficient Extraction

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 19 (part 2)

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