Combinatorial interpretation and proof of Glaisher-Crofton identity
  We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function methodology of modern enumerative combinatorics and their applications to computational problems. 
Pawel Blasiak, Gerard H. E. Duchamp, Andrzej Horzela, Karol A. Penson
math.CO math-ph math.MP