Calkin, Neil J. A curious binomial identity. (English) Zbl 0799.05005 Discrete Math. 131, No. 1-3, 335-337 (1994). Summary: In this communication we shall prove a curious identity of sums of powers of the partial sum of binomial coefficients. Cited in 6 ReviewsCited in 13 Documents MSC: 05A19 Combinatorial identities, bijective combinatorics 05A10 Factorials, binomial coefficients, combinatorial functions Keywords:binomial identity; binomial coefficients PDFBibTeX XMLCite \textit{N. J. Calkin}, Discrete Math. 131, No. 1--3, 335--337 (1994; Zbl 0799.05005) Full Text: DOI Online Encyclopedia of Integer Sequences: a(n) = (n+2)*2^(n-1). a(n) = (n+2)*2^(2*n-1) - (n/2)*binomial(2*n,n). a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^4. a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^5.