[math-fun] Re: favorite theorem

28 Apr 2006

      My favorite "modest" theorem is:

coefficient of x^n/n! in the series expansion of
tan(x)+sec(x) is equal to the number of
up-down permutations of [1,2,...,n].

Namely:
tan(x)+sec(x)=1+(1)*x/1!+(1)*x^2/2!+(2)*x^3/3!+(5)*x^4/4!+...
and 
1;
12;
132, 231;
1324,1423,2314,2413,3412;

Emeric Deutsch