Determine the total number of quintuplets (A,B,C,D,E) of positive integers such that A<=B<=C<=D<=E<=N.
Both analytic and software solution for N=1, 2, ...9,10,...N required.

(In reply to

solution by Charlie)

Kudos for excellent presentation and solution.

I will refer to it when posting the "official" solution.

I will only add a recursive formula for f(n), to facilitate the

numerical evaluation":

**f(1)=1; f(n)=f(n-1)*(f+4)/(n-1)**

hence f(2)=1*6/1=6 f(3)=6*7/2=21 etc matching your results.