Define f(n) = 1! + 2! + ... + n! . Find a recurrence relation f(n + 2) = a(n) f(n + 1) + b(n) f(n), where a(x) and b(x) are polynomials.
Solution
f(n+2) = (n+3) f(n+1) - (n+2) f(n).
45th Putnam 1984
© John Scholes jscholes@kalva.demon.co.uk 7 Jan 2001
