matchbox <- function(n,b) choose(2*n-b,n)*2^(b-2*n) bmatchbox <- function(n,b) b*matchbox(n,b) EM <- function(n) sum(mapply(bmatchbox, n, 0:n)) EM(30) EM <- function(n) (2*n+1)*choose(2*n,n)*2^(-2*n) - 1 EM(30)