French mathematician
Jacques Touchard (1885–1968) was a French mathematician. In 1953, he proved that an odd perfect number must be of the form 12"k" + 1 or 36"k" + 9. In combinatorics and probability theory, he introduced the Touchard polynomials. He is also known for his solution to the ménage problem of counting seating arrangements in which men and women alternate and are not seated next to their spouses.
Touchard's Catalan identity.
The following algebraic identity involving the Catalan numbers
formula_1
is apparently due to Touchard (according to Richard P. Stanley, who mentions it in his panorama article "Exercises on Catalan and Related Numbers" giving an overwhelming plenitude of different definitions for the Catalan numbers).
For "n" ≥ 0 one has
formula_2
Using the generating function
formula_3
it can be proved by algebraic manipulations of generating series that Touchard's identity is 
equivalent to the functional equation
formula_4
satisfied by the Catalan generating series "C"("t").
Further reading.
Canadian Journal of Mathematics 1956, Vol 8, No 3.; Journal in French