where is an Eulerian number and is a binomial coefficient (Worpitzky 1883; Comtet 1974, p. 242).
Worpitzky's Identity
See also
Binomial Sums, Eulerian NumberExplore with Wolfram|Alpha
References
Buhler, J. and Graham, R. "Juggling Drops and Descents." Amer. Math. Monthly 101, 507-519, 1994.Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, 1974.Graham, R. L.; Knuth, D. E.; and Patashnik, O. §6.2 in Concrete Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley, 1994.Stanton, D. Constructive Combinatorics. New York: Springer-Verlag, 1986.Worpitzky, J. "Studien über die Bernoullischen und Eulerischen Zahlen." J. reine angew. Math. 94, 203-232, 1883.Referenced on Wolfram|Alpha
Worpitzky's IdentityCite this as:
Weisstein, Eric W. "Worpitzky's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WorpitzkysIdentity.html